Choice Logics and Their Computational Properties

Bernreiter, Michael; Maly, Jan; Woltran, Stefan

doi:10.24963/ijcai.2021/247

Cited by 5 publications

(8 citation statements)

References 8 publications

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“…Finally, a very interesting question raised by one of the reviewers, is whether the techniques developed in the paper by Charalambidis et al (2021), can also be used to derive a novel and simpler semantics for Qualitative Choice Logic (QCL) (Brewka et al 2004a). Notice that QCL has also recently been investigated with respect to strong equivalence (Bernreiter et al 2021), so the work developed in the present paper may be also relevant in this more general context. sets which are two-valued by definition and therefore the answer sets are the -minimal models among the three-valued models of the program.…”

Section: Examplementioning

confidence: 97%

Strong Equivalence of Logic Programs with Ordered Disjunction: a Logical Perspective

Charalambidis¹,

Nomikos²,

Rondogiannis³

2022

Preprint

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Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs (Brewka 2002;Brewka et al. 2004b), although simple and quite intuitive, is not purely model-theoretic. A consequence of this is that certain properties of programs appear non-trivial to formalize in purely logical terms. An example of this state of affairs is the characterization of the notion of strong equivalence for LPODs (Faber et al. 2008). Although the results of Faber et al. ( 2008) are accurately developed, they fall short of characterizing strong equivalence of LPODs as logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which, as proved by Lifschitz et al. (2001), coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence of LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs introduced by Charalambidis et al. ( 2021), a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs. This work is under consideration for acceptance in TPLP.

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Section: Examplementioning

confidence: 97%

Strong Equivalence of Logic Programs with Ordered Disjunction: a Logical Perspective

Charalambidis¹,

Nomikos²,

Rondogiannis³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Finally, a very interesting question raised by one of the reviewers is whether the techniques developed in the paper by Charalambidis et al (2021) can also be used to derive a novel and simpler semantics for Qualitative Choice Logic (QCL) (Brewka et al 2004a). Notice that QCL has also recently been investigated with respect to strong equivalence (Bernreiter et al 2021), so the work developed in the present paper may be also relevant in this more general context.…”

Section: Examplementioning

confidence: 98%

Strong Equivalence of Logic Programs with Ordered Disjunction: A Logical Perspective

Charalambidis¹,

Nomikos²,

Rondogiannis³

2022

Theory and Practice of Logic Programming

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Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. As a result, certain properties of programs appear non-trivial to formalize in purely logical terms. For example, the current characterization of strong equivalence for LPODs, does not coincide with logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence for LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs, a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs.

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“…First, we formally define the notion of choice logics in accordance with the choice logic framework of [4] before giving concrete examples in the form of QCL and CCL. Finally, we define preferred model entailment.…”

Section: Choice Logicsmentioning

confidence: 99%

“…Next, we define CCL. Note that we follow the revised definition of CCL [4], which differs from the initial specification 1 . Intuitively, given a CCL-formula F #» G it is best to satisfy both F and G, but also acceptable to satisfy only F .…”

Section: Definition 3 the Satisfaction Degree Of A Choice Connectivementioning

confidence: 99%

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Sequent Calculi for Choice Logics

Bernreiter

Lolić

Maly

et al. 2022

Lecture Notes in Computer Science

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Choice logics constitute a family of propositional logics and are used for the representation of preferences, with especially qualitative choice logic (QCL) being an established formalism with numerous applications in artificial intelligence. While computational properties and applications of choice logics have been studied in the literature, only few results are known about the proof-theoretic aspects of their use. We propose a sound and complete sequent calculus for preferred model entailment in QCL, where a formula F is entailed by a QCL-theory T if F is true in all preferred models of T. The calculus is based on labeled sequent and refutation calculi, and can be easily adapted for different purposes. For instance, using the calculus as a cornerstone, calculi for other choice logics such as conjunctive choice logic (CCL) can be obtained in a straightforward way.

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Choice Logics and Their Computational Properties

Cited by 5 publications

References 8 publications

Strong Equivalence of Logic Programs with Ordered Disjunction: a Logical Perspective

Strong Equivalence of Logic Programs with Ordered Disjunction: a Logical Perspective

Strong Equivalence of Logic Programs with Ordered Disjunction: A Logical Perspective

Sequent Calculi for Choice Logics

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