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By
Radev, Slavian
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2 Citations
A logic with normal modal operators and countable infinite conjunctions and disjunctions is introduced. A Hilbert's style axiomatization is proved complete for this logic, as well as for countable sublogics and subtheories. It is also shown that the logic has the interpolation property.
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By
FattorosiBarnaba, M.; Amati, G.
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15 Citations
We present a class of normal modal calculi P_{F}D, whose syntax is endowed with operators M_{r} (and their dual ones, L_{r}), one for each r ε [0,1]: if a is α sentence, M_{r}α is to he read “the probability that a is true is strictly greater than r” and to he evaluated as true or false in every world of a Frestricted probabilistic kripkean model. Every such a model is a kripkean model, enriched by a family of regular (see below) probability evaluations with range in a fixed finite subset F of [0,1]: there is one such a function for every world w, P_{F}(w,), and this allows to evaluate M^{r}a as true in the world w iff p_{F}(w, α) 〉 r.
For every fixed F as before, suitable axioms and rules are displayed, so that the resulting system P_{F}D is complete and compact with respect to the class of all the Frestricted probabilistic kripkean models.
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By
Gärdenfors, Peter
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14 Citations
The purpose of this note is to formulate some weaker versions of the so called Ramsey test that do not entail the following unacceptable consequence
If A and C are already accepted in K, then “if A, then C” is also accepted in K. and to show that these versions still lead to the same triviality result when combined with a preservation criterion.
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By
Hawranek, Jacek
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The present paper is to be considered as a sequel to [1], [2]. It is known that Johansson's minimal logic is not uniform, i.e. there is no single matrix which determines this logic. Moreover, the logic C_{J} is 2uniform. It means that there are two uniform logics C_{1}, C_{2} (each of them is determined by a single matrix) such that the infimum of C_{1} and C_{2} is C_{J}. The aim of this paper is to give a detailed description of the logics C_{1} and C_{2}. It is performed in a latticetheoretical language.
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By
Okada, Mitsuhiro
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We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripketype model theory for WM is given.
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By
Vetulani, Zygmunt
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The aim of the paper is to formalize I. Bellert's (McGill) proposal to characterize distinct nonequivalent readings of quantificationally ambiguous sentences with help of two features: absoluteness and distributiveness. The formalisation makes use of set theoretical and model theoretical standard notions. Foundamental rules, proposed by Bellert, govering the interpretation of cooccurring quantifiers are quoted and outlines of proofs of important derived rules are given.
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By
Lewin, Renato A.
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2 Citations
In [3], O. C. García and W. Taylor make an in depth study of the lattice of interpretability types of varieties first introduced by W. Neumann [5]. In this lattice several varieties are identified so in order to distinguish them and understand the fine structure of the lattice, we propose the study of the interpretations between them, in particular, how many there are and what these are. We prove, among other things, that there are eight interpretations from the variety of Monadic algebras into itself.
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By
Miller, Dale A.
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57 Citations
A structure which generalizes formulas by including substitution terms is used to represent proofs in classical logic. These structures, called expansion trees, can be most easily understood as describing a tautologous substitution instance of a theorem. They also provide a computationally useful representation of classical proofs as firstclass values. As values they are compact and can easily be manipulated and transformed. For example, we present an explicit transformations between expansion tree proofs and cutfree sequential proofs. A theorem prover which represents proofs using expansion trees can use this transformation to present its proofs in more humanreadable form. Also a very simple computation on expansion trees can transform them into Craigstyle linear reasoning and into interpolants when they exist. We have chosen a sublogic of the Simple Theory of Types for our classical logic because it elegantly represents substitutions at all finite types through the use of the typed λcalculus. Since all the prooftheoretic results we shall study depend heavily on properties of substitutions, using this logic has allowed us to strengthen and extend prior results: we are able to prove a strengthen form of the firstorder interpolation theorem as well as provide a correct description of Skolem functions and the Herbrand Universe. The latter are not straightforward generalization of their firstorder definitions.
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By
Slocum, Jonathan
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1 Citations
NABU is a large, multilingual Natural Language Processing (NLP) system being developed at MCC for Human Interface applications. Although the NABU project is not considering Machine Translation (MT) as an implementation domain, it is not unreasonable to suppose that, given our multilingual orientation, some MT problems could be ameliorated if not solved by our theoretical approach. This paper addresses the problem of MT via thecognitive interlingua method, focusing on the representation of the lexicon in such a system, and its accommodation of various sources of knowledge for use by both man and machine: notably, in the latter case, morphology, syntax, and semantics. We propose a new theoretical framework — the NABU Word Lattice — as a means of integrating multiple sources of knowledge in a parsimonious fashion conducive to formal interpretation within, and the construction of, an MT system.
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By
Tong, LoongCheong
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2 Citations
The design of a Translator Workstation is an engineering task involving technical aspects like dictionary organization/retrieval and natural language processing, as well as human aspects like friendly user interface and user accessibility. This paper describes the design and implementation of such a workstation for translating English texts into Malay. Although specifically developed for EnglishMalay translation work, most of the ideas and features presented are language independent. Important issues raised include translation modes and functions, dictionary and thesaurus organization, morphological processing, spelling check and special word processing features.
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By
Majewski, Mirosław
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In this paper we define the relation ≺_{t} of elementary extension of topological models in the language L_{t}and show a Back and Forth criterion for ≺_{t}. We introduce some new operations on partial homeomorphisms preserving Back and Forth properties. Some properties of ≺_{t} are proved by the Back and Forth technique.
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By
Batens, Diderik
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1 Citations
It is shown that the implicational fragment of Anderson and Belnap's R, i.e. Church's weak implicational calculus, is not uniquely characterized by MP (modus ponens), US (uniform substitution), and WDT (Church's weak deduction theorem). It is also shown that no unique logic is characterized by these, but that the addition of further rules results in the implicational fragment of R. A similar result for E is mentioned.
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By
Torrens, Antoni
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14 Citations
We show that the class of all isomorphic images of Boolean Products of members of SR [1] is the class of all archimedean Walgebras. We obtain this result from the characterization of Walgebras which are isomorphic images of Boolean Products of CWalgebras.
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By
Takano, Mitio
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1 Citations
Let EOA be the elementary ontology augmented by an additional axiom ∃S (S ɛ S), and let LS be the monadic secondorder predicate logic. We show that the mapping ϕ which was introduced by V. A. Smirnov is an embedding of EOA into LS. We also give an embedding of LS into EOA.
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By
Furs, S. N.
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A connection between Aristotle's syllogistic and the calculus of relations is investigated. Aristotle's and Gergonne's syllogistics are considered as some algebraic structures. It is proved that Gergonne's syllogistic is isomorphic to closed elements algebra of a proper approximation relation algebra. This isomorphism permits to evaluate Gergonne's syllogisms and also Aristotle's syllogisms, laws of conversion and relations in the “square of oppositions” by means of regular computations with Boolean matrices.
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By
Gerla, Giangiacomo
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6 Citations
If X is set and L a lattice, then an Lsubset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for Lsubsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate Lsubsets with no “more precise” decidable versions and classical subsets whose unique shaded decidable versions are the Lsubsets almosteverywhere indeterminate.
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By
Nirenburg, Sergei; Carbonell, Jaime
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2 Citations
We present an integrated knowledge representation system for natural language processing (NLP) whose main distinguishing feature is its emphasis on encoding not only the usual propositional structure of the utterances in the input text, but also capturing an entire complex of nonpropositional — discourse, attitudinal, and other pragmatic — meanings that NL texts always carry. The need for discourse pragmatics, together with generic semantic information, is demonstrated in the context of anaphoric and definite noun phrase resolution for accurate machine translation. The major types of requisite pragmatic knowledge are presented, and an extension of a framebased formalism developed in the context of the TRANSLATOR system is proposed as a firstpass codification of the integrated knowledge base.
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By
Takano, Mitio
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7 Citations
Those formulas which are valid in every Kripke model having constant domain whose base is the ordered set R of real numbers (or, the ordered set Q of rational numbers) are characterized syntactically.
By
Ho, Nguyen Cat; Rasiowa, Helena
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1 Citations
SemiPost algebras have been introduced and investigated in [6]. This paper is devoted to semiPost subalgebras and homomorphisms. Characterization of semiPost subalgebras and homomorphisms, relationships between subalgebras and homomorphisms of semiPost algebras and of generalized Post algebras are examined.
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By
Pal'chunov, D. E.
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10 Citations
In the paper all countable Boolean algebras with m distinguished. ideals having countablycategorical elementary theory are described and constructed. From the obtained characterization it follows that all countablycategorical elementary theories of Boolean algebras with distinguished ideals are finiteaxiomatizable, decidable and, consequently, their countable models are strongly constructivizable.
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By
Gajda, Adam; Krynicki, Michał; Szczerba, Lesław
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5 Citations
We say that a semantical function Г is correlated with a syntactical function F iff for any structure A and any sentence ϕ we have A ⊧ Fϕ ↔ ΓA ⊧ ϕ.
It is proved that for a syntactical function F there is a semantical function Г correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function Г there is a syntactical function F correlated with Г iff for any finitely axiomatizable class X the class Г^{−1}X is also finitely axiomatizable (i.e. iff Г is continuous in model class topology).
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By
Ho, Nguyen Cat; Rasiowa, Helena
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3 Citations
In this paper, semiPost algebras are introduced and investigated. The generalized Post algebras are subcases of semiPost algebras. The so called primitive Post constants constitute an arbitrary partially ordered set, not necessarily connected as in the case of the generalized Post algebras examined in [3]. By this generalization, semiPost products can be defined. It is also shown that the class of all semiPost algebras is closed under these products and that every semiPost algebra is a semiPost product of some generalized Post algebras.
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By
Jongh, Dick H. J.; Montagna, Franco
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2 Citations
To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by BernardiMontagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovaytype) completeness theorem with respect to PA is obtained for LR.
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By
Smirnov, Vladimir A.
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1 Citations
There is given the proof of strict embedding of Leśniewski's elementary ontology into monadic secondorder calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom ∃ S (S ɛ S) is strictly embeddable into monadic secondorder calculus of predicates which provides a formalization of the classes of all formulas valid in all nonempty domains.
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By
D'Ottaviano, Ítala M. L.
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6 Citations
The Joint NonTrivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J_{3}theories. These theories are threevalued with more than one distinguished truthvalue, reflect certain aspects of model type logics and can. be paraconsistent. J_{3}theories were introduced in the author's doctoral dissertation.
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By
Daniels, Charles B.
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3 Citations
In [2] a semantics for implication is offered that makes use of ‘stories’ — sets of sentences assembled under various constraints. Sentences are evaluated at an ‘actual’ world and in each member of a set of stories. A sentence B is true in a story s just when B ε s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the firstorder language of [2] is extended by the addition of the operator ‘the story ... says that ...’, as in ‘The story Flashman among the Redskins says that Flashman met Sitting Bull’. The resulting language is shown to be sound and complete.
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By
Novák, Vilém
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45 Citations
This paper is an attempt to develop the manyvalued firstorder fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 〈0, 1〉 of reals. These are special cases of a residuated lattice 〈L, ∨, ∧, ⊗, →, 1, 0〉. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the firstorder fuzzy logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional nary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the firstorder fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Gödel's completeness theorems are proved which confirm that the firstorder fuzzy logic is also semantically complete.
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By
Gillis, Philip D.
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1 Citations
The purpose of this research was to determine whether computeraided instruction may be effectively utilized in stimulating prewriting composition when the CAI is based upon (1) conceptual (cognitive) strategies, (2) “datadriven” guidance (resulting from CAE techniques), and (3) recent findings in tutorial strategies research. If this specifically designed CAI is as good a means of prewriting instruction as personal tutoring and a better means than classroom instruction, then the practical and economical implications may be weighed in a decision to use such techniques. Fortythree college freshmen in three basic writing classes participated in this study. One class was exposed to a CAI medium, the other two either to a human tutor or to classroom instruction. A computeraided evaluation of previous essays provided focus, and other intellectual processing cues provided information on an expository topic; this “database” was then used to construct a CAI program to encourage “specificity” and “depth of intellectual processing“ in students' prewriting composition. The program also possessed and was designed to provide “conceptual guidance” through the use of five heuristic procedures; thus it contained two key elements that a human tutor would possess in working with a topic—knowledge of the topic, and a means for eliciting that knowledge from the tutee. The second treatment method used consisted of instruction by human tutors, utilizing the same methodology. The control for the study consisted of a classroom instruction group. Results showed the CAI group demonstrating gains in every category of measurement utilized in this study, and its performances was significantly better than both the tutorial group on two of the posttest measures. The CAI group was superior, through not significantly, on posttest performances in every category used in the study except fluency.
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