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Confalonieri, Roberto; Nieves, Juan Carlos; Osorio, Mauricio; VázquezSalceda, Javier
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In this paper, we show how the formalism of Logic Programs with Ordered Disjunction (LPODs) and Possibilistic Answer Set Programming (PASP) can be merged into the single framework of Logic Programs with Possibilistic Ordered Disjunction (LPPODs). The LPPODs framework embeds in a unified way several aspects of commonsense reasoning, nonmonotonocity, preferences, and uncertainty, where each part is underpinned by a well established formalism. On one hand, from LPODs it inherits the distinctive feature of expressing contextdependent qualitative preferences among different alternatives (modeled as the atoms of a logic program). On the other hand, PASP allows for qualitative certainty statements about the rules themselves (modeled as necessity values according to possibilistic logic) to be captured. In this way, the LPPODs framework supports a reasoning which is nonmonotonic, preference and uncertaintyaware. The LPPODs syntax allows for the specification of (1) preferences among the exceptions to default rules, and (2) necessity values about the certainty of program rules. As a result, preferences and uncertainty can be used to select the preferred uncertain default rules of an LPPOD and, consequently, to order its possibilistic answer sets. Furthermore, we describe the implementation of an ASPbased solver able to compute the LPPODs semantics.
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Osorio, Mauricio; Navarro, Juan Antonio
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We develop some ideas in order to obtain a nonmonotonic reasoning system based on the modal logic S4. As a consequence we show how to express the well known answer set semantics using a restricted fragment of modal formulas. Moreover, by considering the full set of modal formulas, we obtain an interesting generalization of answer sets for logic programs with modal connectives. We also depict, by the use of examples, possible applications of this inference system.
It is also possible to replace the modal logic S4 with any other modal logic to obtain similar nonmonotonic systems. We even consider the use of multimodal logics in order to model the knowledge and beliefs of agents in a scenario where their ability to reason about each other’s knowledge is relevant. Our results clearly state interesting links between answer sets, modal logics and multiagent systems.
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Ayala, Gerardo; Ortiz, Magdalena; Osorio, Mauricio
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This paper presents the pertinence of the use of the Answer Set Programming (ASP) formalism for developing a computational model of a software agent for Computer Supported Collaborative Learning (CSCL) environments. This analytic model is based on a representation of for agent’s beliefs about the learner and the domain, together with the corresponding inference system with the appropriate rules to derive new beliefs about the capabilities of the learner, and its use in order to support effective collaboration and maintain learning possibilities for the group members. The model provides a representation of the structural knowledge frontier and the social knowledge frontier of the learner, which are the components for the definition of the learner’s zone of proximal development (zpd). Based on the zpd of its learner the agent can propose her a learning task and maintain the zpd for the learner in the group. The complete code of the model is presented in the declarative language of DLV, a logic programming language for implementing ASP models.
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Nieves, Juan Carlos; Osorio, Mauricio; Zepeda, Claudia
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2 Citations
Extensionbased argumentation semantics is a successful approach for performing nonmonotonic reasoning based on argumentation theory. An interesting property of some extensionbased argumentation semantics is that these semantics can be characterized in terms of logic programming semantics. In this paper, we present novel results in this topic. In particular, we show that one can induce an argumentation semantics (that we call Stratified Argumentation Semantics) based on a logic programming semantics that is based on stratified minimal models. We show that the stratified argumentation semantics overcome some problems of extensionbased argumentation semantics based on admissible sets and we show that it coincides with the argumentation semantics CF2.
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Osorio, Mauricio; Jayaraman, Bharat
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7 Citations
Setgrouping and aggregation are powerful operations of practical interest in database query languages. An aggregate operation is a function that maps a set to some value, e.g., the maximum or minimum in the set, the cardinality of this set, the summation of all its members, etc. Since aggregate operations are typically nonmonotonic in nature, recursive programs making use of aggregate operations must be suitably restricted in order that they have a welldefined meaning. In a recent paper we showed that partialorder clauses provide a wellstructured means of formulating aggregate operations with recursion. In this paper, we consider the problem of expressing partialorder programs via negationasfailure (NF), a wellknown nonmonotonic operation in logic programming. We show a natural translation of partialorder programs to normal logic programs: Anycostmonotonic partialorder programsP is translated to astratified normal program such that the declarative semantics ofP is defined as the stratified semantics of the translated program. The ability to effect such a translation is significant because the resulting normal programs do not make any explicit use of theaggregation capability, yet they are concise and intuitive. The success of this translation is due to the fact that the translated program is a stratified normal program. That would not be the case for other more general classes of programs thancostmonotonic partialorder programs. We therefore develop in stages a refined translation scheme that does not require the translated programs to be stratified, but requires the use of a suitable semantics. The class of normal programs originating from this refined translation scheme is itself interesting: Every program in this class has a clear intended total model, although these programs are in general neither stratified nor callconsistent, and do not have a stable model. The partial model given by the wellfounded semantics is consistent with the intended total model and the extended well founded semantics,WFS^{+}, defines the intended model. Since there is a welldefined and efficient operational semantics for partialorder programs^{14, 15, 21)} we conclude that the gap between expression of a problem and computing its solution can be reduced with the right level of notation.
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Osorio, Mauricio
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2 Citations
Partialorder programming is introduced in [JOM95] where it is shown how partialorder clauses help render clear and concise formulations to a different kind of problems, in particular optimization problems. In this paper we present some more examples that we can model using partialorder clauses and we also introduce its FixPoint semantics. We show that this paradigm and standard logic programming can be naturally integrated in one paradigm. We also discuss WFSCOMP, a new semantics for normal programs, that can be used to give the meaning of general normal+partialorder programs via a translation.
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Osorio, Mauricio; Zacarías, Fernando
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1 Citations
We have studied the update operator ⊕ defined in [4] without tautologies and we have observed that satisfies an interesting property. This property is similar to one postulate proposed by AGM but, in this case for nonmonotonic logic and that we called WIS. Also, we consider other five additional basic properties about update programs and we show that ⊕ satisfies them. So, this work continues the analysis about the AGM postulates with respect to operator ⊕ under the refinated view that includes knowledge and beliefs that we began in a recent previous paper and that satisfies the WIS property for closed programs under tautologies.
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Olmos, Ivan; Gonzalez, Jesus A.; Osorio, Mauricio
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Finding common patterns is an important problem for several computer science subfields such as Machine Learning (ML) and Data Mining (DM). When we use graphbased representations, we need the Subgraph Isomorphism (SI) operation for finding common patterns. In this research we present a new approach to find a SI using a list code based representation without candidate generation. We implement a step by step expansion model with a widthdepth search. The proposed approach is suitable to work with labeled and unlabeled graphs, with directed and undirected edges. Our experiments show a promising method to be used with scalable graph matching.
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By
Confalonieri, Roberto; Nieves, Juan Carlos; Osorio, Mauricio; VázquezSalceda, Javier
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3 Citations
Logic programs with ordered disjunction (or LPODs) have shown to be a flexible specification language able to model and reason about preferences in a natural way. However, in some realistic applications which use user preferences in the reasoning, information can be pervaded with vagueness and a preferenceaware reasoning process that can handle uncertainty is required. In this paper we address these issues, and we propose a framework which combines LPODs and possibilistic logic to be able to deal with a reasoning process that is preferenceaware, nonmonotonic, and uncertain. We define a possibilistic semantics for capturing logic programs with possibilistic ordered disjunction (or LPPODs) which is a generalization of the original semantics. Moreover, we present several transformation rules which can be used to optimize LPODs and LPPODs code and we show how the semantics of LPODs and the possibilistic semantics of LPPODs are invariant w.r.t. these transformations.
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Osorio, Mauricio; Nieves, Juan Carlos; Zacarias, Fernando; Saucedo, Erika
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We introduce the new paradigm of HighLevel NonMonotonic reasoning (HLNM). This paradigm is the consolidation of our recent results on disjunctions, sets, explicit and implicit negation, and partialorder clauses. We show how these concepts are integrated in a natural way into the standard logic programming framework. For this purpose, we present several well known examples from the literature that motivate the need of this new paradigm. Finally, we define a declarative semantics for HLNM reasoning.
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Osorio, Mauricio; Nieves, Juan Carlos
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The stable semantics has become a prime candidate for knowledge representation and reasoning. The rules associated with propositional logic programs and the stable semantics are not expressive enough to let one write concise optimization programs. We propose an extension to the language of logic programs that allows one to express optimization problems in a suitable well. In earlier work we defined the declarative semantics for partial order clauses. The main contribution of our paper is the following: First, we define the language of our extended paradigm as well as its declarative semantics. Our declarative semantics is based on translating partial order clauses into normal programs and the using the stable semantics as the intended meaning of the original program. Second, we propose an operational semantics for our paradigm. Our experimental results show that our approach is more efficient than using the well known system SMODELS over the translated program.
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Osorio, Mauricio; Navarro, Juan Antonio; Arrazola, José
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1 Citations
AProlog, Answer Set Programming or Stable Model Programming, is an important outcome of the theoretical work on Nonmonotonic Reasoning and AI applications of Logic Programming in the last 15 years. In the full version of this paper we study interesting applications of logic in the field of answer sets.
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Osorio, Mauricio; Borja, Veronica; Arrazola, Jose
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In order to really understand all aspects of logicbased program development of different semantics, it would be useful to have a common solid logical foundation. The stable semantics has one already based on intuitionistic logic I and using the notion of completions. Since S4 expresses I then the stable semantics can be fully represented in S4. We propose the same approach to define extensions of the WFS semantics. We distinguish a particular semantics that we call ASWFS wich is defined over general propositional theories, can be defined via completions using S4. Interesting ASWFS seems to satisfy most of the principles of a well behaved semantics. Our general goal is to propose S4 and completions to study the formal behavior of different semantics.
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Osorio, Mauricio; Jayaraman, Bharat
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The three most wellknown semantics for negation in the logic programming framework are Clark’s completion [Cla78], the stable semantics [GL88], and the wellfounded semantics [vGRS91]. Clark’s completion (COMP) was the first proposal to give a formal meaning to negation as failure. However, it is now accepted that COMP does not always captures the meaning of a logic program. Despite its computational and structural advantages, the wellfounded semantics (WFS) is considered much too weak for real applications. The stable semantics (STABLE), on the other hand, is so strong that many programs become inconsistent. We present in this paper examples to support these claims, and we introduce a new semantics, called CWFS, which is as powerful as COMP in inferring positive literals and as powerful as WFS in inferring negative literals. Due to its particular construction, CWFS helps to understand the relationship among COMP, WFS, and STABLE. We also discuss some implementation issues of CWFS.
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Osorio, Mauricio; Carballido, José Luis; Zepeda, Claudia
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We show how to use the Answer Set Programming (ASP) tool called clasp to prove that there exists a unique threevalued paraconsistent logic that satisfies the substitution property and is sound with respect to da Costa C_{ω} logic.
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Osorio, Mauricio; Jayaraman, Bharat
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3 Citations
Setgrouping and aggregation are powerful nonmonotonic operations of practical interest in database query languages. We consider the problem of expressing aggregation via negation as failure (NF). We study this problem in the framework of partialorder clauses introduced in [JOM95]. We show a translation of partialorder programs to normal programs that is very natural: Any costmonotonic partialorder program P becomes a stratified normal program transl(P) such that the declarative semantics of P is equivalent to the stratified semantics of transl(P). The ability to effect such a translation is significant because the resulting normal programs do not make any explicit use of the aggregation capability, yet they are concise and intuitive. The success of this translation is due to the fact that the translated program is a stratified normal program. That would not be the case for other more general classes of programs than costmonotonic partialorder programs. We therefore investigate a second (and more natural) translation that does not require the translated programs to be stratified, but requires the use of a suitable NF strategy. The class of normal programs originating from this translation is itself interesting. Every program in this class has a clear intended total model, although these programs are in general not stratified and not even callconsistent and do not have a stable model. The partial model given by the wellfounded semantics is consistent with the intended total model and the extended well founded semantics WFS^{+} indeed defines the intended model. Since there is a welldefined and efficient operational semantics for partialorder programs [JOM95, JM95] we conclude that the gap between expression of a problem and computing its solution can be reduced with the right level of notation.
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Osorio, Mauricio; Díaz, Juan; Santoyo, Alejandro
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Dung’s abstract argumentation frameworks has been object of intense study not just for its relationship with logical reasoning but also for its uses within artificial intelligence. One research branch in abstract argumentation has focused on finding new methods for computing its different semantics. We present a novel method, to the best of our knowledge, for computing preferred semantics using 01 integer programming, and also experimentally compare it with two answer set programming approaches. Our results indicate that this new method performed well.
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Osorio, Mauricio; Borja, Verónica; Arrazola, José
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1 Citations
In order to really understand all aspects of logicbased program development of different semantics, it would be useful to have a common solid logical foundation.
The stable semantics are based on G_{3} but we show that stable semantics can be fully represented in the three valued logic of Łukasiewicz . We construct a particular semantics that we call Ł_{3}WFS which is defined over general propositional theories, can be defined via three valued logic of Łukasiewicz. Interesting Ł_{3}WFS seems to satisfy most of the principles of a well behaved semantics. Hence we propose the three valued Łukasiewicz logic to model WFS, extensions of WFS, and the Stable semantics.
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Nieves, Juan Carlos; Osorio, Mauricio; Cortés, Ulises
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8 Citations
In this paper by considering answer set programming approach and some basic ideas from possibilistic logic, we introduce a possibilistic disjunctive logic programming approach able to deal with reasoning under uncertain and incomplete information. Our approach permits to use explicitly labels like possible, probable, plausible, etc., for capturing the incomplete state of a belief in a disjunctive logic program.
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Estrada, Oscar; Arrazola, José; Osorio, Mauricio
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We define what we call “Possibilistic Intuitionistic Logic (PIL)”; We present results analogous to those of the wellknown intuitionistic logic, such as a Deduction Theorem, a Generalized version of the Deduction Theorem, a Cut Rule, a weak version of a Refutation Theorem, a Substitution Theorem and Glivenko’s Theorem.
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Osorio, Mauricio; Zepeda, Claudia
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In this paper we introduce preference rules which allow us to specify preferences as an ordering among the possible solutions of a problem. Our approach allow us to express preferences for general theories. The formalism used to develop our work is Answer Set Programming. Two distinct semantics for preference logic programs are proposed. Finally, some properties that help us to understand these semantics are also presented.
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Osorio, Mauricio; Carballido, José Luis; Zepeda, Claudia
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We present an extension of GLukG, a logic that was introduced in [8] as a threevalued logic under the name of G′_{3}. GLukG is a paraconsistent logic defined in terms of 15 axioms, which serves as the formalism to define the pstable semantics of logic programming. We introduce a new axiomatic system, NGLukG, a paraconsistent logic that possesses strong negation. We use the 5valued logic N′_{5}, which is a conservative extension of GLukG, to help us to prove that NGLukG is an extension of GLukG. NGLukG can be used as the formalism to define the pstable semantics as well as the stable semantics.
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Osorio, Mauricio; Borja, Veronica; Arrazola, Jose
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In order to really understand all aspects of logicbased program development of different semantics, it would be useful to have a common solid logical foundation. The stable semantics has one already based on intuitionistic logic I and using the notion of completions. Since S4 expresses I then the stable semantics can be fully represented in S4. We propose the same approach to define extensions of the WFS semantics. We distinguish a particular semantics that we call ASWFS wich is defined over general propositional theories, can be defined via completions using S4. Interesting ASWFS seems to satisfy most of the principles of a well behaved semantics. Our general goal is to propose S4 and completions to study the formal behavior of different semantics.
Keywords: Stable semantics, WFS, FOUR, Modal logics.
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Osorio, Mauricio; Zepeda, Claudia; Carballido, José Luis
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We propose an engineering approach for assembling argumentation theory with a preference approach, which allows us to give as input an argumentation problem with preferences and return the stable argumentation extensions that fulfill the preferences.
By
Osorio, Mauricio; Carballido, José Luis; Zepeda, Claudia; Cruz, Zenaida
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Argumentation theory studies the fundamental mechanism humans use in argumentation and explores ways to implement this mechanism on computers. Dung’s approach, presented in [9], is a unifying framework which has played an influential role on argumentation research. In this paper, we show that, a logic programming semantics, called MM^{r}, can be used to characterize the preferred argumentation semantics defined by Dung in [9]. The MM^{r} [12] is based on the the minimal model semantics. The characterization of this argumentation semantics by the MM^{r} semantics suggests a new perception of this argumentation semantics in terms of logic foundations.
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AcostaGuadarrama, Juan Carlos; DávilaPérez, Rogelio; Osorio, Mauricio; Zaldivar, Victor Hugo
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Metaphors are natural language constructions that play an important role in the way human beings communicate knowledge and understand the world. Some formal philosophers such as Searle and Lakoff claim that the semantic analysis of expressions that involve fictional stories and metaphors are examples of the inadequacy of using predicate logic for the analysis of the meaning of language. D’Hanis proposes that using predicate logic in combination of nonmonotonic reasoning is possible to interpret metaphorical expressions. In this paper, we introduce an approach for modelling metaphorical thinking using a particular form of logic programming called answer set programming (ASP). ASP essentially enhances the logical apparatus of predicate calculus by introducing mechanisms such as negation as a failure that enable the system to accomplish nonmonotonic reasoning. We show that using ASP is possible to model the meaning of some expressions involving metaphorical constructions and the implementation of metaphorical reasoning mechanisms that could be a great addition to any knowledgebased application.
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Osorio, Mauricio; Nieves, Juan Carlos
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1 Citations
Recently, a good set of logic programming semantics has been defined for capturing possibilistic logic program. Practically all of them follow a credulous reasoning approach. This means that given a possibilistic logic program one can infer a set of possibilistic models. However, sometimes it is desirable to associate just one possibilistic model to a given possibilistic logic program. One of the main implications of having just one model associated to a possibilistic logic program is that one can perform queries directly to a possibilistic program and answering these queries in accordance with this model.
In this paper, we introduce an extension of the WellFounded Semantics, which represents a sceptical reasoning approach, in order to capture possibilistic logic programs. We will show that our new semantics can be considered as an approximation of the possibilistic semantics based on the answer set semantics and the pstable semantic. A relevant feature of the introduced semantics is that it is polynomial time computable.
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Osorio, Mauricio; Navarro, Juan A.; Arrazola, José
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10 Citations
We study the notion of strong equivalence between two Answer Set programs and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in intuitionistic or classical logic. We present some program transformations for disjunctive programs, which can be used to simplify the structure of programs and reduce their size. These transformations are shown to be of interest for both computational and theoretical reasons. Then we propose how to generalize such transformations to deal with free programs (which allow the use of default negation in the head of clauses). We also present a linear time transformation that can reduce an augmented logic program (which allows nested expressions in both the head and body of clauses) to a program consisting only of standard disjunctive clauses and constraints.
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Osorio, Mauricio; Zacarias, Fernando
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3 Citations
We introduce the paradigm of HighLevel Logic Programming. This paradigm is the consolidation of our recent results on disjunctions, sets, partialorder clauses and aggregation. We show how these concepts are integrated in a natural way into the standard logic programming framework. For this purpose, we present several well known examples from the literature that support this claim. Our approach to define the declarative semantics of HLL (HighLevel Logic) programs consists on a translation of them to datalog disjunctive programs and then to use D1WFSCOMP.
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Osorio, Mauricio; Zepeda, Claudia
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6 Citations
In case intelligent agents get new knowledge and this knowledge must be added or updated to their knowledge base, it is important to avoid inconsistencies. Currently there are several approaches dealing with updates. In this paper, we propose a semantics for update sequences. We start introducing the notion of minimal generalized (MG) pstable models that, as we argue is interesting by itself. Based on MG pstable models we construct our update semantics. In this work, we also use some representative examples to compare our update semantics to other known update semantics and observe some advantages of it.
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Osorio, Mauricio; Nieves, Juan Carlos
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4 Citations
Uncertain information is present in many real applications e.g., medical domain, weather forecast, etc. The most common approaches for leading with this information are based on probability however some times; it is difficult to find suitable probabilities about some events. In this paper, we present a possibilistic logic programming approach which is based on possibilistic logic and PStable semantics. Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and Pstable Semantics is a solid semantics which emerges from the fusion of nonmonotonic reasoning and logic programming; moreover it is able to express answer set semantics, and has strong connections with paraconsistent logics.
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Osorio, Mauricio; Carballido, J. L.; Zepeda, C.; Castellanos, J. A.
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By weakening an inference rule satisfied by logic daC, we define a new paraconsistent logic (daC^{'}), which is weaker than logic
$${{\mathbb{Z}}}$$
and G′_{3}, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism. Besides, daC^{'} helps to understand the relationships among other logics, in particular daC,
$${{\mathbb{Z}}}$$
and PH1.
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