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By
Cheung, Percy; Fung, Pascale
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2 Citations
Codeswitching is very common among bilingual speakers. Spoken queries by
these speakers are typically in mixed language. In this paper, we propose an unsupervised
method for mixedlanguage query understanding, using only a monolingual corpus
and a bilingual dictionary. Secondarylanguage words mixed in a primarylanguage query
are translated into words in the primary language. We found that using a single disambiguation
feature for translation is more effective than using multiple features, provided
this feature is based on the most salient seedword, chosen automatically by conﬁdence
scoring. We propose and compare four types of disambiguation features that are based on
context seedwords. A baseline method uses the nearest neighboring seedword as disambiguation
feature. Multiplecontext seedword voting is also proposed in order to enlarge
the context window. On the other hand, merely using the inversedistance as weights on
context words degrades the performance as it runs counter to the potential underlying
syntactic relations between words. Our ﬁnal proposal is a solution that uses multiplecontext
seedwords and the translation candidates of all mixed language words to select a
single most salient seedword for translation disambiguation. The translation disambiguation
accuracy for this feature is at 83.7% for all words in the ATIS spontaneous speech
query database, and 66.7% for content words.
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By
Han, ChungHye; Palmer, Martha
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4 Citations
This paper describes a novel approach to morphological tagging for Korean, an agglutinative language with a very productive inflectional system. The tagger takes raw text as input and returns a lemmatized and morphologically disambiguated output for each word: the lemma is labeled with a partofspeech (POS) tag and the inflections are labeled with inflectional tags. Unlike the standard approach to tagging for morphologically complex languages, in our proposed approach the tagging phase precedes the analysis phase. It comprises a trigrambased tagging component followed by a morphological rule application component, obtaining 95% precision and recall on unseen test data.
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By
Guessoum, Ahmed; Zantout, Rached
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4 Citations
Abstract.
This paper presents a methodology for evaluating Arabic Machine Translation (MT) systems. We are specifically interested in evaluating lexical coverage, grammatical coverage, semantic correctness and pronoun resolution correctness. The methodology presented is statistical and is based on earlier work on evaluating MT lexicons in which the idea of the importance of a specific word sense to a given application domain and how its presence or absence in the lexicon affects the MT system’s lexical quality, which in turn will affect the overall system output quality. The same idea is used in this paper and generalized so as to apply to grammatical coverage, semantic correctness and correctness of pronoun resolution. The approach adopted in this paper has been implemented and applied to evaluating four EnglishArabic commercial MT systems. The results of the evaluation of these systems are presented for the domain of the Internet and Arabization.
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By
Odintsov, Sergei P.
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4 Citations
Two logics L_{1} and L_{2} are negatively equivalent if for any set of formulas X and any negated formula ¬ϕ, ¬ϕ can be deduced from the set of hypotheses X in L_{1} if and only if it can be done in L_{2}. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.
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By
Veloso, Paulo A. S.; Veloso, Sheila R. M.
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3 Citations
Logics for “generally” were introduced for handling assertions with vague notions,such as “generally”, “most”, “several”, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a firstorder theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical firstorder logic to reason about consequence in ultrafilter logic.
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By
Schmidt, Renate A.; Tishkovsky, Dmitry; Hustadt, Ullrich
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6 Citations
This paper considers a new class of agent dynamic logics which provide a formal means of specifying and reasoning about the agents’ activities and informational, motivational and practical aspects of the behaviour of the agents. We present a Hilbertstyle deductive system for a basic agent dynamic logic and consider a number of extensions of this logic with axiom schemata formalising interactions between knowledge and commitment (expressing an agent’ s awareness of her commitments), and interactions between knowledge and actions (expressing no learning and persistence of knowledge after actions). The deductive systems are proved sound and complete with respect to a Kripkestyle semantics. Each of the considered logics is shown to have the small model property and therefore decidable.
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By
Morin, Emmanuel; Jacquemin, Christian
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20 Citations
Recent developments in computational terminology call for the design of multiple and complementary tools for the acquisition, the structuring and the exploitation of terminological data. This paper proposes to bridge the gap between term acquisition and thesaurus construction by offering a framework for automatic structuring of multiword candidate terms with the help of corpusbased links between singleword terms. First, we present a system for corpusbased acquisition of terminological relationships through discursive patterns. This system is built on previous work on automatic extraction of hyponymy links through shallow parsing. Second, we show how hypernym links between singleword terms can be extended to semantic links between multiword terms through corpusbased extraction of semantic variants. The induced hierarchy is incomplete but provides an automatic generalization of singleword terms relations to multiword terms that are pervasive in technical thesauri and corpora.
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By
Lindén, Krister
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1 Citations
Word sense disambiguation automatically determines the appropriate senses of a word in context. We have previously shown that selforganized document maps have properties similar to a largescale semantic structure that is useful for word sense disambiguation. This work evaluates the impact of different linguistic features on selforganized document maps for word sense disambiguation. The features evaluated are various qualitative features, e.g. partofspeech and syntactic labels, and quantitative features, e.g. cutoff levels for word frequency. It is shown that linguistic features help make contextual information explicit. If the training corpus is large even contextually weak features, such as base forms, will act in concert to produce sense distinctions in a statistically significant way. However, the most important features are syntactic dependency relations and base forms annotated with part of speech or syntactic labels. We achieve 62.9% ± 0.73% correct results on the fine grained lexical task of the English SENSEVAL2 data. On the 96.7% of the test cases which need no backoff to the most frequent sense we achieve 65.7% correct results.
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By
Alanzi, Fawaz S.
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In this paper, two new models for generating diacritics for Arabic names are proposed. The first proposed model is called Ngram model. It is a stochastic model that is based on generating a corpus database of Ngrams extracted from a large database of names with their corresponding probability according to an Ngram position in a text (Bhal et al., 1983). i.e., the probability that an Ngram has happened in a position x, where x can be the first, second,... or ith position in the text. Replacing the Ngrams with their patterns extends the first model to the second proposed stochastic model. It is called the Envelope model. These two proposed models are unique in being the first attempt to solve the problem in Arabic text diacritics generation using linguistic constraints stochastic approaches that are neither grammatical nor pure lexical based (Merialdo, 1991; Ney and Essen, 1991; SchukatTalamazzini et al., 1992; Witschel and Niedermair, 1992). This methodology helps in reducing size and complexity of software implementation of the proposed models and makes it easier to update and port across different platforms.
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By
Hammo, Bassam; Abuleil, Saleem; Lytinen, Steven; Evens, Martha
Show all (4)
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14 Citations
The World Wide Web (WWW) today is so vast that it has become more and more difficult to find answers to questions using standard search engines. Current search engines can return ranked lists of documents, but they do not deliver direct answers to the user. The goal of Open Domain Question Answering (QA) systems is to take a natural language question, understand the meaning of the question, and present a short answer as a response based on a repository of information. In this paper we present QARAB, a QA system that combines techniques from Information Retrieval and Natural Language Processing. This combination enables domain independence. The system takes natural language questions expressed in the Arabic language and attempts to provide short answers in Arabic. To do so, it attempts to discover what the user wants by analyzing the question and a variety of candidate answers from a linguistic point of view.
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By
Rietveld, Toni; hout, Roeland Van; Ernestus, Mirjam
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8 Citations
. This paper discusses some pitfalls in corpus research and suggests solutions on the basis of examples and computer simulations. We first address reliability problems in language transcriptions, agreement between transcribers, and how disagreements can be dealt with. We then show that the frequencies of occurrence obtained from a corpus cannot always be analyzed with the traditional χ^{2} test, as corpus data are often not sequentially independent and unit independent. Next, we stress the relevance of the power of statistical tests, and the sizes of statistically significant effects. Finally, we point out that a ttest based on log odds often provides a better alternative to a χ^{2} analysis based on frequency counts.
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By
Volkov, M. V.
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2 Citations
We exhibit a 10element semigroup Q such that the question “Does a given quasiidentity hold inQ?” is coNPcomplete while the question “Does a given identity hold inQ?” can be answered in linear time.
By
Patton, Jon M.; Can, Fazli
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6 Citations
We analyze four İnce Memed novels of Yaşar Kemal using six style markers: “most frequent words,” “syllable counts,” “word type – or part of speech – information,” “sentence length in terms of words,” “word length in text,” and “word length in vocabulary.” For analysis we divide each novel into five thousand word text blocks and count the frequencies of each style marker in these blocks. The style markers showing the best separation are “most frequent words” and “sentence lengths.” We use stepwise discriminant analysis to determine the best discriminators of each style marker. We then use these markers in cross validation based discriminant analysis. Further investigation based on multiple analysis of variance (MANOVA) reveals how the attributes of each style marker group distinguish among the volumes.
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By
Adaricheva, K. V.; Gorbunov, V. A.
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We study the structure of algebraic τclosed subsets of an algebraic lattice L, where τ is some Browerian binary relation on L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruenceNoetherian quasivarieties.
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By
Budkin, Alexander
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11 Citations
The dominion of a subalgebra H in an universal algebra A (in a class
$$\mathcal{M}$$
) is the set of all elements
$$a \in A$$
such that for all homomorphisms
$$f,g:A \to B \in \mathcal{M}$$
if f, g coincide on H, then a^{f} = a^{g}. We investigate the connection between dominions and quasivarieties. We show that if a class
$$\mathcal{M}$$
is closed under ultraproducts, then the dominion in
$$\mathcal{M}$$
is equal to the dominion in a quasivariety generated by
$$\mathcal{M}$$
. Also we find conditions when dominions in a universal algebra form a lattice and study this lattice.
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By
Burmeister, Peter
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Based on existence equations, quasivarieties of heterogeneous partial algebras have the same algebraic description as those of total algebras. Because of the restriction of the valuations to the free variables of a formula — the usual reference to the needed variables e.g. for identities (in order to get useful and manageable results) is essentially replaced here by the use of the “logical Craig projections” — already varieties of heterogeneous partial algebras behave to some extent rather like quasivarieties than having the properties known from varieties of total homogeneous algebras. It is one of the main aims of this note to make this more explicit. On the other hand we want to list several results known for quasivarieties of heterogeneous partial algebras — and adopt them to the extended signature — after having recalled the language and the main concepts necessary for the understanding of the results.
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By
Caicedo, Xavier
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11 Citations
An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable.
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By
Auinger, Karl; Gomes, Gracinda M. S.; Gould, Victoria; Steinberg, Benjamin
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5 Citations
The technique of covers is now well established in semigroup theory. The idea is, given a semigroup S, to find a semigroup Ŝ having a better understood structure than that of S, and an onto morphism θ of a specific kind from Ŝ to S. With the right conditions on θ, the behaviour of S is closely linked to that of Ŝ. If S is finite one aims to choose a finite Ŝ. The celebrated results for inverse semigroups of McAlister in the 1970’s form the flagship of this theory.
Weakly left quasiample semigroups form a quasivariety (of algebras of type(2, 1)), properly containing the classes of groups, and of inverse, left ample, and weakly left ample semigroups. We show how the existence of finite proper covers for semigroups in this quasivariety is a consequence of Ash’s powerful theorem for pointlike sets. Our approach is to obtain a cover Ŝ of a weakly left quasiample semigroup S as a subalgebra of S × G, where G is a group. It follows immediately from the fact that weakly left quasiample semigroups form a quasivariety, that Ŝ is weakly left quasiample. We can then specialise our covering results to the quasivarieties of weakly left ample, and left ample semigroups. The latter have natural representations as (2, 1)subalgebras of partial (oneone) transformations, where the unary operation takes a transformation α to the identity map in the domain of α. In the final part of this paper we consider representations of weakly left quasiample semigroups.
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By
Maróti, Miklós; McKenzie, Ralph
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9 Citations
Let
$$\mathcal{K}$$
be a finite collection of finite algebras of finite signature such that SP(
$$\mathcal{K}$$
) has meet semidistributive congruence lattices. We prove that there exists a finite collection
$$\mathcal{K}$$
_{1} of finite algebras of the same signature,
$$\mathcal{K}_1 \supseteq \mathcal{K}$$
, such that SP(
$$\mathcal{K}$$
_{1}) is finitely axiomatizable.We show also that if
$$HS(\mathcal{K}) \subseteq SP(\mathcal{K})$$
, then SP(
$$\mathcal{K}$$
_{1}) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.
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By
Czelakowski, J.; Pigozzi, D.
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8 Citations
A deductive system
$$\mathcal{S}$$
(in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas
$$\{ \left\langle {\alpha ,\beta } \right\rangle :T,\alpha \vdash s \beta and T,\beta \vdash s \alpha \} ,$$
is a congruence relation on the formula algebra. The multiterm deductiondetachment theorem is a natural generalization of the deduction theorem of the classical and intuitionistic propositional calculi (IPC) in which a finite system of possibly compound formulas collectively plays the role of the implication connective of IPC. We investigate the deductive structure of Fregean deductive systems with the multiterm deductiondetachment theorem within the framework of abstract algebraic logic. It is shown that each deductive system of this kind has a deductive structure very close to that of the implicational fragment of IPC. Moreover, it is algebraizable and the algebraic structure of its equivalent quasivariety is very close to that of the variety of Hilbert algebras. The equivalent quasivariety is however not in general a variety. This gives an example of a relatively pointregular, congruenceorderable, and congruencedistributive quasivariety that fails to be a variety, and provides what apparently is the first evidence of a significant difference between the multiterm deductiondetachment theorem and the more familiar form of the theorem where there is a single implication connective.
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By
Davey, Brian A.; Haviar, Miroslav
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3 Citations
This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasivariety to other generating algebras. Detailed calculations are given for the quasivariety
$$\mathbb{I}\mathbb{S}\mathbb{P}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle}$}}{4} )$$
of Kleene algebras and the quasivarieties
$$B$$
_{n} of pseudocomplemented distributive lattices (n ≥ 1).
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By
Lee, Changki; Lee, Gary Geunbae; Seo, Jungyun
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2 Citations
This paper presents an automatic construction of Korean WordNet from preexisting lexical resources. We develop a set of automatic word sense disambiguation techniques to link a Korean word sense collected from a bilingual machinereadable dictionary to a single corresponding English WordNet synset. We show how individual links provided by each word sense disambiguation method can be nonlinearly combined to produce a Korean WordNet from existing English WordNet for nouns.
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By
Holzer, Richard
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1 Citations
In this paper some properties of epirepresentations and Schmidtcongruence relations of orthomodular partial algebras are investigated and an infinite list of OMAepisubdirectly irreducible orthomodular partial algebras will be constructed.
By
Matczak, K.; Romanowska, A.
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7 Citations
The paper describes the isomorphic lattices of quasivarieties of commutative quasigroup modes and of cancellative commutative binary modes. Each quasivariety is characterised by providing a quasiequational basis. A structural description is also given. Both lattices are uncountable and distributive.
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By
Adámek, Jiří
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1 Citations
Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, −) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.
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By
Vernitski, Alexei
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4 Citations
In this paper, we concentrate on finite quasivarieties (i.e. classes of finite algebras defined by quasiidentities). We present a motivation for studying finite quasivarieties. We introduce a new type of conditions that is well suited for defining finite quasivarieties and compare these new conditions with quasiidentities.
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By
Hoehnke, HansJürgen
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Quasiequational logic concerns with a completeness theorem, i. e. a list of general syntactical rules such that, being given a set of graded quasiequations Q, the closure Cl Q = Qeq Fun Q can be derived from
$$Q \subseteq (X:QE)$$
by the given rules. Those rules do exist, because our consideration could be embedded into the logic of first order language. But, we look for special (“quasiequational”) rules. Suitable rules were already established for the (nonfunctorial) case of partial algebras in Definition 3.1.2 of [27], p. 108, and [28], p. 102. (For the case of total algebras, see [35].) So, one has to translate these rules to the (functorial) language of partial theories
$$\underline T \in \left {\underline {\mathcal{T}h} } \right$$
.
Surprisingly enough, partial theories can be replaced up to isomorphisms by partial “Dale” monoids (cf. Section 3), which, in the total case are ordinary monoids.
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By
Koubek, V.; Sichler, J.
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2 Citations
Adams and Dziobiak proved that any finitetofinite universal quasivariety must be Quniversal, and then asked whether a somewhat weaker hypothesis could lead to the same conclusion. We show that their original hypothesis cannot be weakened to its naturally extreme form.
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By
Blok, W. J.; Raftery, J. G.
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13 Citations
The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deductiondetachment theorem for the fragments without disjunction. Together with results of Sobociński, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations.
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By
Adams, M. E.; adaricheva, K. V.; Dziobiak, W.; Kravchenko, A. V.
Show all (4)
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14 Citations
The BirkhoffMaltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the BirkhoffMaltsev problem are also considered, including ones that stem from the theory of propositional logics.
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By
Cohen, Ariel
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20 Citations
It is widely agreed that generics tolerate exceptions. It turns out, however, thatexceptions are tolerated only so long as they do not violate homogeneity:when the exceptions are not concentrated in a salient “chunk” of the domain ofthe generic. The criterion for salience of a chunk is cognitive: it is dependent onthe way in which the domain is mentally represented. Findings of psychologicalexperiments about the ways in which different domains are represented, and thefactors affecting such representations, account for judgments of generic sentences,facts which cannot be explained by linguistics alone.The reason for the homogeneity requirement itself is, in turn, also dependenton cognitive considerations. Generics express default rules, and psychologicalfindings have shown that, the more homogeneous the domain, the easier it isfor subjects to infer rules about it. Thus, cognitive results form a crucial part of a comprehensive account of the meaningof a linguistic expression.
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By
Ogihara, Toshiyuki
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7 Citations
This article discusses what may be referred to as ``adjectival relatives''in Japanese and related constructions in other languages (such asadjectival passives in English). The most intriguing characteristicof this construction is that the verb contained in it occurs in the pasttense form, but its primary role is to describe a state that obtains atthe local evaluation time, rather than the past event that producedthis state. In fact, in some cases, the putative event that presumablyproduced the target state is nonexistent, and the entire constructionreceives a purely stative interpretation. In other words, it is possiblefor an adjectival relative to describe a target state without having itstriggering event. The proposal I put forth in the article states that whatI refer to as an adjectival relative does not have a clausal structure.It rather has a verbal projection (technically a Tense Phrase, or TP). Mod(the modifier head) then combined with TP to yield a MP (modifierphrase), which denotes a property of states that appear to have resultedfrom an event the verb describes. In order to reach this conclusion, I adopttwo additional ideas: (i) Kratzer's (1996) idea that the socalled externalargument of a verb is not really its argument at all; (ii) direct causationdoes not have to be overtly represented in natural language syntax (Bittner1999). Having incorporated these two ideas, the proposal explains therelation between the state that the adjectival relative describes and theputative event as a modal one, thereby accounting for the nonexistenceof putative past events in some examples.
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By
Romero, Maribel; Han, ChungHye
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53 Citations
Preposed negation yes/no (yn)questions like Doesn't Johndrink? necessarily carry the implicature that the speaker thinks Johndrinks, whereas nonpreposed negation ynquestions like DoesJohn not drink? do not necessarily trigger this implicature. Furthermore,preposed negation ynquestions have a reading “doublechecking” pand a reading “doublechecking” ≠ p, as in Isn't Jane comingtoo? and in Isn't Jane coming either? respectively. We present otherynquestions that raise parallel implicatures and argue that, in allthe cases, the presence of an epistemic conversational operator VERUMderives the existence and content of the implicature as well as thep/≠ pambiguity.
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By
Casillas, Arantza; Martínez, Raquel
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This paper reports on a method for exploiting a bitext as the primary linguistic information source for the design of a generation environment for specialized bilingual documentation. The paper discusses such issues as Text Encoding Initiative (TEI), proposals for specialized corpus tagging, text segmentation and alignment of translation units and their allocation into translation memories, Document Type Definition (DTD), abstraction from tagged texts, and DTD deployment for bilingual text generation. The parallel corpus used for experimentation has two main features:
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By
Pałasińska, Katarzyna
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Motivated by a question of W. Rautenberg, we prove that any matrix that is termequivalent to the wellknown nonfinitely based matrix of A. Wroński is itself also nonfinitely based.
By
Roeper, Peter
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Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of information. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truthfunctional part of the logic as given, the present paper proposes a semantics entirely based on epistemic states and operations on these states. The semantics is accompanied by a syntactic treatment of conditional logic which is formally similar to Gentzen's sequent formulation of natural deduction rules. Three of David Lewis's systems of conditional logic are represented. The formulations are attractive by virtue of their transparency and simplicity.
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By
Pambuccian, Victor
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6 Citations
We provide a quantifierfree axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose axioms are also at most 4variable universal sentences. We also provide an axiom system for plane hyperbolic geometry in Tarski's language L_{B≡} which might be the simplest possible one in that language.
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By
Trentin, Guglielmo
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4 Citations
Many teachers adopt networked collaborative learning strategies even though these approaches systematically increase the time needed to deal with a given subject. “But who's making them do it?”. Probably there has to be a return on investment, in terms of time and obviously in terms of educational results, which justifies that commitment. After surveying the particular features of two experimental projects based on networked collaborative learning, the paper will then offer a series of thoughts triggered by observation of the results and the dynamics generated by this specific approach. The purpose of these thoughts is to identify some key factors that make it possible to measure the real added value produced by network collaboration in terms of the acquisition of skills, knowledge, methods and attitudes that go beyond the “mere” learning of contents (however fundamental this may be). And it is precisely on the basis of these considerations that teachers usually answer the above question, explaining “who (or what) made them do it!”.
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By
Lin, JoWang
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6 Citations
A recent popular analysis of English indefinites isthat they involve a choice function mechanism in their semantic interpretation. However,there are diversified views regarding how intermediate scope readings should be dealt withand which level(s) existential closure should apply to. This paper attempts to make acontribution to this debate by examining existential polarity whphrases in Chinese. I showthat unlike the behaviors of polarity indefinites in St'át'imcets reported by Matthewson(1999), intermediate scope readings are possible for polarity whphrases in Chinese but aresubject to some locality conditions. I suggest that implicit arguments of choice functionsmight have a parametric value the choice of which affects availability of intermediate readings.The findings in this paper thus revive the possibility, rejected by Matthewson (1999), that thechoice function mechanism may vary from language to language or from indefinite NPs in onelanguage to indefinite NPs in another language or even from one type of indefiniteNP to another type of indefinite NP within the same language.
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By
Koons, Robert C.
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Threevalued (strongKleene) modal logic provides the foundation for a new approach to formalizing causal explanation as a relation between partial situations. The approach makes finegrained distinctions between aspects of events, even between aspects that are equivalent in classical logic. The framework can accommodate a variety of ontologies concerning the relata of causal explanation. I argue, however, for a tripartite ontology of objects corresponding to sentential nominals: facts, tropes (or facta or states of affairs), and situations (or events). I axiomatize the relations and use canonical models to demonstrate completeness.
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By
Spencer, Matthew; Howe, Christopher
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12 Citations
To reconstruct a stemma or do any other kind of statistical analysis of a text tradition, one needs accurate data on the variants occurring at each location in each witness. These data are usually obtained from computer collation programs. Existing programs either collate every witness against a base text or divide all texts up into segments as long as the longest variant phrase at each point. These methods do not give ideal data for stemma reconstruction. We describe a better collation algorithm (progressive multiple alignment) that collates all witnesses word by word without a base text, adding groups of witnesses one at a time, starting with the most closely related pair.
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By
Dayal, Veneeta
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69 Citations
This paper explores the link between number marking and(in)definiteness in nominals and their interpretation. Differencesbetween bare singulars and plurals in languages without determinersare explained by treating bare nominals as kind terms. Differencesarise, it is argued, because singular and plural kinds relatedifferently to their instantiations. In languages with determiners,singular kinds typically occur with the definite determiner, butplural/mass kinds can be bare in some languages and definite inothers. An account of singular kinds in terms of taxonomic readingsis proposed, with number marking playing a crucial role inexplaining the obligatory presence of the determiner. The variationbetween languages with respect to plural/mass kinds is explained bypositing a universal scale of definiteness, with individual languageschoosing different cutoff points for lexicalization of the definitedeterminer. The possibility of further crosslinguistic variation isalso considered.
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By
Essid, Joe
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A few ideas from film theory, most notably Eisenstein's concept of montage, can improve students' understanding of hypertexts and lessen their resistance to openended, nonlinear narratives. These structural characteristics, so frustrating to many new readers of hypertext, can also be found in popular and experimental films. In particular, Godfrey Reggio's (1983) documentary Koyaanisqatsi provides a good starting point for merging hypertext and film theory. Koyaanisqatsi not only broke new ground for documentary film; its structure also resembles Landow's model for an axial hypertext. At the same time, techniques pioneered by Landow, Joyce, Guyer, and others involved in creating and critiquing hypertext can be used to examine film. Having students look closely at Koyaanisqatsi's composition allows them to become amateur cinematographers, who now possess software for breaking a film down and examining its composition, montage, transitions, subliminal messages, and motifs – a process that may then be applied to hypertext.
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Kamide, Norihiro
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13 Citations
A new logic, quantized intuitionistic linear logic (QILL), is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's (commutative) involutive quantales. Some cutfree sequent calculi with a new property “quantization principle” and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.
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By
van Rooy, Robert
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51 Citations
In this paper I will discuss why (un) marked expressionstypically get an (un)marked interpretation: Horn'sdivision of pragmatic labor. It is argued that it is aconventional fact that we use language this way.This convention will be explained in terms ofthe equilibria of signalling games introduced byLewis (1969), but now in an evolutionary setting. Iwill also relate this signalling game analysis withParikh's (1991, 2000, 2001) gametheoretical analysis ofsuccessful communication, which in turn is compared withBlutner's: 2000) bidirectional optimality theory.
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By
Unger, Melvin
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Bach's cantatas are particularly rich in text imagery, and they typically employ chromatic melodies to accentuate the more piquant literary images, especially in recitatives. Heretofore theories about the intentionality of Bach's compositional choices in this regard have necessarily remained conjectural. In the following study, an objective measurement of pitch diversity in the vocal lines of Bach's church cantata recitatives in relation to literary themes was made possible with specially designed computer software allowing pertinent information to be entered efficiently into a relational database. Because the software tracked not only the 90,000 pitches constituting the vocal lines of these movements but also other attributes (e.g., overall length, presence or absence of accompaniment, opening and closing keys, chronological position, among others), interrelationships among the various attributes could be examined. Findings demonstrate clear correlation between pitch diversity and the degree of affective tension implied by particular textual subjects. While the findings do not prove exclusive causation (other factors such as tonal and structural considerations, social occasion, and evolution of style can also play a role), they do link the two elements, especially in light of Bach's method of composition as documented by Robert Marshall. This study is important for its systematic and comprehensive approach, its findings giving definition and clarity to commonly held generalizations about the relationships between melodic chromaticism (of which pitch diversity is an important aspect and indicator) and textual content. Furthermore, the software holds promise for additional studies of Bach's pitch materials and for studies in other stylistic contexts.
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By
Skvortsov, Dmitrij
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5 Citations
An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (‘levelwise uniform’ trees) and establish the finite axiomatizability criterion for this case.
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By
Kowalski, Tomasz
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16 Citations
We prove that all semisimple varieties of FL_{ew}algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL_{ew}algebras follows. It matches exactly a natural classification of logics over FL_{ew} proposed by H. Ono.
By
Wroński, Andrzej
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The equivalence connective in Łukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =x−y of a positive cone of a commutative ℓgroup. We make some observations on logically motivated algebraic structures involving the distance function.
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By
Galatos, Nikolaos; Raftery, James G.
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35 Citations
Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x^{2}≤x but fails to preserve the contraction property x≤x^{2}. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and selfdual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem) decidability of the negationfree axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t.
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By
Belardinelli, Francesco; Jipsen, Peter; Ono, Hiroakira
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19 Citations
We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasicompletion of these Gentzen structures. It is shown that the quasicompletion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and OkadaTerui [17].
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By
Jónsson, Bjarni; Tsinakis, Constantine
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13 Citations
The central result of this paper provides a simple equational basis for the join, IRL∨LG, of the variety LG of latticeordered groups (ℓgroups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRL∨LG=IRL×LG. In the process of deriving our result, we will obtain simple axiomatic bases for other products of classes of residuated structures, including the class IRL×_{s}LG, consisting of all semidirect products of members of IRL by members of LG. We conclude the paper by presenting a general method for constructing such semidirect products, including wreath products.
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By
Berman, Joel; Blok, W. J.
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14 Citations
Hoop residuation algebras are the {→, 1}subreducts of hoops; they include Hilbert algebras and the {→, 1}reducts of MValgebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of kpotent hoop residuation algebras. The assumption of kpotency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {→, 1}reduct of the same finite MValgebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusionexclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MValgebras and of hoops).
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By
Ginzburg, Jonathan; Cooper, Robin
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29 Citations
The paper investigates an elliptical construction, Clarification Ellipsis, that occurs in dialogue. We suggest that this provides data that demonstrates that updates resulting from utterances cannot be defined in purely semantic terms, contrary to the prevailing assumptions of existing approaches to dynamic semantics. We offer a computationally oriented analysis of the resolution of ellipsis in certain cases of dialogue clarification. We show that this goes beyond standard techniques used in anaphora and ellipsis resolution and requires operations on highly structured, linguistically heterogeneous representations. We characterize these operations and the representations on which they operate. We offer an analysis couched in a version of HeadDriven Phrase Structure Grammar combined with a theory of information states (IS) in dialogue. We sketch an algorithm for the process of utterance integration in IS which leads to grounding or clarification. The account proposed here has direct applications to the theory of attitude reports, an issue which is explored briefly in the concluding remarks of the paper.
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By
Venema, Yde
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6 Citations
We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame, or, topological relational structure. These characterizations involve a special binary toporeachability relation on the dual structure; we call a point u a toporoot of the dual structure if every ultrafilter is toporeachable from u. We prove that a boolean algebra with operators is simple iff every point in the dual structure is a toporoot; and that it is subdirectly irreducible iff the collection of toporoots is open and nonempty in the Stone topology on the dual structure iff this collection has nonempty interior in that topology.
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By
Schechter, Eric
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Relevant logic is a proper subset of classical logic. It does not include among its theorems any of
positive paradox A→ (B → A)
mingle A→ (A → A)
linear order (A → B) ∨ (B → A)
unrelated extremes (A ∧Ā) → (B ∨ B¯)
This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.
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By
Holmes, M. Randall
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3 Citations
Three systems of “double extension set theory” have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameterfree version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a selfcontained exposition of their properties is given, sufficient to develop the inconsistency proofs.
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By
Correia, Fabrice
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14 Citations
In 1977, R. B. Angell presented a logic for analytic containment, a notion of “relevant” implication stronger than Anderson and Belnap's entailment. In this paper I provide for the first time the logic of first degree analytic containment, as presented in [2] and [3], with a semantical characterization—leaving higher degree systems for future investigations. The semantical framework I introduce for this purpose involves a special sort of truthpredicates, which apply to pairs of collections of formulas instead of individual formulas, and which behave in some respects like Gentzen's sequents. This semantics captures very general properties of the truthfunctional connectives, and for that reason it may be used to model a vast range of logics. I briefly illustrate the point with classical consequence and Anderson and Belnap's “tautological entailments”.
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By
Hanson, Sven Ove
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2 Citations
The logic of an “ought” operator O is contranegative with respect to an underlying preference relation ≥ if it satisfies the property Op & (¬p)≥(¬q) →Oq. Here the condition that ≥ is interpolative ((p≥ (p∨q) ≥q) ∨ (q≥ (p∨q) ≥p)) is shown to be necessary and sufficient for all ≥contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & Oq→O(p&q)) and disjunctive division (O(p&q) →Op ∨ Oq).
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By
Bohnemeyer, Jürgen; Swift, Mary
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35 Citations
There are languages – e.g., German, Inuktitut, andRussian – in which the aspectual reference of clausesdepends on the telicity of their event predicates. Weargue that in such languages, clauses or verb phrasesnot overtly marked for viewpoint aspect implicateor entail ‘event realization’, a property akin toParsons's (1990) `culmination'. The aspectualreference associated with the use of clauses notovertly marked for aspect is computed in accordancewith the dependence of realization conditions ontelicity and in line with principles of Gricean pragmatics.We formalize event realization and capture thetelicitydependent patterns of aspectual reference onwhich it is based by combining Krifka's (1989, 1992,1998) event lattices with a modeltheoreticinterpretation of Klein's (1994) theory of tense andaspect. The latter permits us to treat the `topic times'of aspectual operators as temporal constraints on event realization.
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By
Terui, Kazushige
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15 Citations
In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a nontraditional hybrid sequent calculus which is required for formulating LLL.
In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total inLAST.
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By
Pambuccian, Victor
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3 Citations
As with the development of several logical notions, it is shown that the concept of resourceconsciousness, i. e. the concern over the number of times that a given sentence is used in the proof of another sentence, has its origin in the foundations of geometry, predating its appearence in logical circles as BCKlogic or affine logic.
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By
Sauerland, Uli
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139 Citations
This article develops a Gricean account for the computation of scalarimplicatures in cases where one scalar term is in the scope ofanother. It shows that a crossproduct of two quantitative scalesyields the appropriate scale for many such cases. One exception iscases involving disjunction. For these, I propose an analysis that makesuse of a novel, partially ordered quantitative scale for disjunction andcapitalizes on the idea that implicatures may have different epistemic status.
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By
Diaconescu, Răzvan
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23 Citations
We formulate a general institutionindependent (i.e. independent of the details of the actual logic formalised as institution) version of the Craig Interpolation Theorem and prove it in dependence of Birkhoffstyle axiomatizability properties of the actual logic.
We formalise Birkhoffstyle axiomatizability within the general abstract model theoretic framework of institution theory by the novel concept of Birkhoff institution.
Our proof destills a set of conditons behind the Craig Interpolation Property, which are easy to establish in the applications. Together with the generality of our approach, this leads to a wide range of applications for our result, including conventional and nonconventional logics (many of them from algebraic specification theory), such as general algebra, classical model theory, partial algebra, rewriting logic, membership algebra, etc. all of them in various versions and with various types of sentences (including infinitary ones). In dependence of axiomatizability properties many other applications are expected for various institutions or logics.
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By
Tufiş, Dan; Barbu, Ana Maria; Ion, Radu
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3 Citations
The paper describes our recent developments in automatic extraction of translation equivalents from parallel corpora. We describe three increasingly complex algorithms: a simple baseline iterative method, and two noniterative more elaborated versions. While the baseline algorithm is mainly described for illustrative purposes, the noniterative algorithms outline the use of different working hypotheses which may be motivated by different kinds of applications and to some extent by the languages concerned. The first two algorithms rely on crosslingual POS preservation, while with the third one POS invariance is not an extraction condition. The evaluation of the algorithms was conducted on three different corpora and several pairs of languages.
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By
Cybulka, Jolanta; Martinek, Jacek
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The purpose of our research is to consider how the paradigms of EuroWordNet and SIMPLE linguistic projects on the one hand and the OIL methodology on the other hand may affect each other. OIL (Ontology Inference Layer) aims at implementing the ``semantic'' Web idea and is based on the notion of ontology, which is also employed in EuroWordNet and SIMPLE. In both latter projects the meanings of words are partially described by means of the finite sets of relations to other meanings of words, whereas in OIL the user is free to define the arbitrary relations of this kind.The relations considered in EuroWordNet and SIMPLE were defined on the basis of a careful observation of the large linguistic area, andt hey aim at reflecting the meaning as precisely as possible, therefore it seems useful to merge them with OIL. Moreover, the valuable feature of OIL is its formal language with precisely defined semantics. All things considered, we suggest how certain EuroWordNet and SIMPLE definitions may be expressed in OIL.
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By
Wilks, Yorick
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2 Citations
The paper explores the notions of text ownership and its partial inverse, plagiarism, and asks how close or different they are from a procedural point of view that might seek to establish either of these properties. The emphasis is on procedures rather than on the conventional subject division of authorship studies, plagiarism detection etc. We use, as a particular example, our research on the notion of computational detection of text rewriting, in the benign sense of a standard journalist's adaptation of the Press Association newsfeed. The conclusion is that, whatever may be the case in copyright law, procedural detection and establishment of the ownership is a complex and vexed matter. Behind the paper is an unspoken appeal to return to an earlier historical phase, one where texts were normally rewritten and rewritten again and the ownership of text by an individual was a less clear matter than in historically recent times.
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By
Louwerse, Max M.
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9 Citations
Idiolects are persondependent similarities in language use. They imply that texts by one author show more similarities in language use than texts between authors. Sociolects, on the other hand, are groupdependent similarities in language use. They imply that texts by a group of authors, for instance in terms of gender or time period, share more similarities within a group than between groups. Although idiolects and sociolects are commonly used terms in the humanities, they have not been investigated a great deal from corpus and computational linguistic points of view. To test several idiolect and sociolect hypotheses a factorial combination was used of time period (Modernism, Realism), gender of author (male, female) and author (Eliot, Dickens, Woolf, Joyce) totaling 16 corresponding literary texts. In a series of corpus linguistic studies using Boolean and vector models, no conclusive evidence was found for the selected idiolect and sociolect hypotheses. In final analyses testing the semantics within each literary text, this lack of evidence was explained by the low homogeneity within a literary text.
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By
Brown, Susan; Grundy, Isobel; Clements, Patricia; Elio, Renée; Balazs, Sharon; Cameron, Rebecca
Show all (6)
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2 Citations
This paper explores theoretical and practical aspects of intertextuality, in relation to the highly interpretative <intertextuality> tag within the SGML tagset developed by the Orlando Project for its history of women's writing in the British Isles. Arguing that the concept of intertextuality is both crucial to and poses particular challenges to the creation of an encoding scheme for literary historical text, it outlines the ways in which the project's tags address broader issues of intertextuality. The paper then describes the specific <intertextuality> tag in detail, and argues on the basis of provisional results drawn from the Orlando Project's textbase that despite the impossibility of tracking intertextuality exhaustively or devising a tagset that completely disambiguates the concept, this tag provides useful pathways through the textbase and valuable departure points for further inquiry. Finally, the paper argues that the challenges to notions of rigour posed by the concept of intertextuality can help us fruitfully to examine some of the suppositions (gendered and other) that we bring to electronic text markup.
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By
Whithaus, Carl
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2 Citations
This essay traces a distinction between computermediated writing environments that are tools for correcting student prose and those that are media for communication. This distinction has its roots in the influence of behavioral science on teaching machines and computeraided writing instruction during the 1960s and 1970s. By looking at the development of the timeshared, interactive, computercontrolled, information television (TICCIT) and early human–computer interaction (HCI) research, this essay demonstrates that hardware and software systems had the potential to work as both tools and media. The influence of this double logic is not only historical but also has implications for postsecondary writing instruction in the age of Microsoft Word, ETS's erater, and the “reading/assessment” software tools being developed by Knowledge Analysis Technologies (KAT). This essay challenges composition researchers and computational linguists to develop pedagogies and software systems that acknowledge writing environments as situated within the logic of both tools for correction and media for communication.
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By
Rigo, Michel
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For a given numeration system U, a set X of integers is said to be Ustarfree if the language of the normalized Urepresentations of the elements in X is starfree. Adapting a result of McNaughton and Papert, we give a firstorder logical characterization of these sets for various numeration systems including integer base systems and the Fibonacci system. For kary systems, the problem of the base dependence of this property is also studied. Finally, the case of kadic systems is developed.
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By
Smessaert, Hans; Ter Meulen, Alice G. B.
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3 Citations
Validity of dynamic temporal reasoning is semantically characterized for Englishand Dutch aspectual adverbs in Discourse Representation Theory. This dynamicperspective determines how the content needs to be revised and what informationis preserved across updates, when the order of premises is considered relevant.Resetting contextual parameters relies on modelling the basic aspectual polaritytransitions and temporal reasoning extensionally. For intensional aspectual adverbialsthe speaker's attitudes regarding past alternatives to and possible continuations of thecurrent state come into play. Additional considerations are offered for generalizing thissystem to the full logical space for linguistic universals, lexicalized quite differently inDutch and English.
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By
Cohen, Ariel
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15 Citations
While opinions on the semantic analysis of generics vary widely, most scholars agree that generics have a quasiuniversal flavor. However, there are cases where generics receive what appears to be an existentialinterpretation. For example, B's response is true, even though only theplatypus and the echidna lay eggs:
(1) A: Birds lay eggs. B: Mammals lay eggs too.
In this paper I propose a uniform account of the semantics of generics,which accounts for their quasiexistential readings as well as for their more familiar quasiuniversal ones. Generics are focussensitiveoperators: their domain is restricted by a set of alternatives, which may be provided by focus. I claim that, unlike otherfocussensitive operators, generics may, but do not have to, associate with focus. When alternatives are introduced, either by focus or by other means, generics get their usual quasiuniversal readings. But when no alternatives are introduced, quasiexistential readings result.I argue that generics, unlike adverbs of quantification, do not introduce tripartite structures directly, but are initially interpreted as cases ofdirect kind predication. Only when this interpretation fails to make sense, the phonologically null generic quantifier is derived, and tripartite structures result. This twolevel interpretation has the effect that while adverbs of quantification require focus to determine which elements go to the restrictor and which to the nuclear scope, and hence must associate with focus, generics do not, and hence may fail to associate with focus, resulting in quasiexistential readings.
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By
Meixner, Uwe
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3 Citations
I argue (1) that it is not philosophically significant whether causation is linguistically represented by a predicate or by a sentence connective; (2) that there is no philosophically significant distinction between event and statesofaffairscausation; (3) that there is indeed a philosophically significant distinction between agent and eventcausation, and that eventcausation must be regarded as an analog of agentcausation. Developing this point, I argue that eventcausation's being in the image of agentcausation requires, mainly, (a) that the cause is temporally prior to the effect, (b) that the cause necessitates (is sufficient with necessity) for the effect. Causal necessity is explained as a derivative of nomological necessity, and finally, via a definition of the causal sentence connective, the logic of eventcausation is shown to be a part of temporal modal logic.
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By
Tamminga, Allard
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3 Citations
We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extralogical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGMstyle characterizations of these operations follow.
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By
Kostrzycka, Zofia; Zaionc, Marek
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15 Citations
For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.
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By
Odintsov, Sergei P.
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27 Citations
N4lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4lattices showing that the structure of an arbitrary N4lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4lattices are described.
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By
Gawron, Jean Mark; Kehler, Andrew
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10 Citations
We provide a semantic analysis of respective readings, including butnot limited to the interpretation of examples containing the adverbrespectively, which accounts for a number of facts that haveeither proven difficult for previous studies or heretofore goneunnoticed in the literature. The analysis introduces the new notionsof property sum and proposition sum which integrate smoothly with existing analyses of plurals and distributivity. The analysis also admits of a straightforward account of previouslyunacknowledged examples involving fillergap dependencies that areproblematic for contemporary syntactic theories. Ramifications anddirections for future research are discussed.
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By
Litak, Tadeusz
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In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some Σ
$$ \subseteq $$
L and some
$$\varphi \notin L,\varphi $$
cannot be separated from Σ by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. Even above Grz it is possible to find a continuum of such logics, which immediately implies the existence of a continuum of neighbourhoodincomplete Grz logics. Similar results can be proved for Löb logics. In addition, completely incomplete logics above Grz may be found uniformly as a result of failures of some admissible rule of a special kind.
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