Combining Equilibrium Logic and Dynamic Logic

Cerro, Luís Fariñas del; Herzig, Andreas; Su, Ezgi Iraz

doi:10.1007/978-3-642-40564-8_30

Cited by 4 publications

(6 citation statements)

References 13 publications

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“…We believe that epistemic here-and-there logic EHT provides a suitable basis for further extensions of answer-set programs with modal concepts, which is a research avenue that has recently arisen some interest specifically for extensions by temporal [42][43][44][45][46][47] and dynamic [48] concepts. A first step could be the extension from single-agent epistemic logic to multi-agent epistemic logic.…”

Section: Resultsmentioning

confidence: 99%

Autoepistemic equilibrium logic and epistemic specifications

Cerro

Herzig

2020

Artificial Intelligence

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Epistemic specifications extend disjunctive answer-set programs by an epistemic modal operator that may occur in the body of rules. Their semantics is in terms of world views, which are sets of answer sets, and the idea is that the epistemic modal operator quantifies over these answer sets. Several such semantics were proposed in the literature. We here propose a new semantics that is based on the logic of here-and-there: we add epistemic modal operators to its language and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from epistemic here-and-there models in exactly the same way as Pearce's equilibrium models are obtained from here-and-there models, viz. by minimising truth; they provide an epistemic extension of equilibrium logic. The latter are obtained from the former by maximising the set of epistemic possibilities, and they provide a new semantics for Gelfond's epistemic specifications. For both semantics we establish a strong equivalence result: we characterise strong equivalence of two epistemic programs by means of logical equivalence in epistemic here-and-there logic. We finally compare our approach to the existing semantics of epistemic specifications and discuss which formalisms provide more intuitive results by pointing out some formal properties a semantics proposal should satisfy.

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Section: Resultsmentioning

confidence: 99%

Autoepistemic equilibrium logic and epistemic specifications

Cerro

Herzig

2020

Artificial Intelligence

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“…Beyond the embedding of CL-PC that we have recalled in Sect. 3.5, the central role of DL-PA is confirmed by DL-PA accounts of update and revision operations [54], belief merging operations [63], abstract argumentation theories and their modification [33], and answer-set programs and their modification [36]; moreover, its epistemic extension, public announcement logic with assignments, solves the epistemic frame problem [114,115]. As to logics with epistemic operators, we have recalled that S5 is inadequate as a logic of knowledge and should be replaced by S4.2; furthermore, we have shown that the definition of common knowledge by means of the Greatest Fixpoint Axiom GFP(CK J ) is at least questionable.…”

Section: Summary and Research Challengesmentioning

confidence: 89%

“…Its applicability to update and revision operations, planning tasks, argumentation theory and answer-set programming has been demonstrated recently [33,36,54,62]. In the rest of the section we show that it captures a logic of ability.…”

Section: Reiter's Solution To the Frame Problemmentioning

confidence: 99%

Logics of knowledge and action: critical analysis and challenges

Herzig

2014

Auton Agent Multi-Agent Syst

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15176 Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Logics of knowledge and action: critical analysis and challenges Andreas HerzigAbstract We overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges.

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“…An epistemic interpretation I is called an Sworld view of an ELP Π iff I = AS (Π I S ) and I = ∅. Various semantics S have been defined over the years and most of them can be characterized by reducts Π I S , either over sets of interpretations (as above) or over the set of elit(Π) that are satisfied by I (Kahl 2014;del Cerro, Herzig, and Su 2015;Shen and Eiter 2016;Son et al 2017;Kahl and Leclerc 2018;Faber, Morak, and Woltran 2019;Morak 2019;Cabalar, Fandinno, and del Cerro 2020). A concise summary can be found in (Leclerc and Kahl 2018).…”

Section: Preliminariesmentioning

confidence: 99%

“…e.g. (Gelfond 2011;Truszczynski 2011;Kahl 2014;del Cerro, Herzig, and Su 2015;Shen and Eiter 2016;Son et al 2017;Kahl and Leclerc 2018;Faber, Morak, and Woltran 2019;Morak 2019)), with refinements of the semantics and proposals of new language features. Further, the development of efficient solving systems is underway with several efficient systems now available (Kahl et al 2015;Son et al 2017;Bichler, Morak, and Woltran 2020).…”

Section: Introductionmentioning

confidence: 99%

Evaluating Epistemic Logic Programs via Answer Set Programming with Quantifiers

Faber

Morak

2023

AAAI

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In this paper we introduce a simple way to evaluate epistemic logic programs by means of answer set programming with quantifiers, a recently proposed extension of answer set programming. The method can easily be adapted for most of the many semantics that were proposed for epistemic logic programs. We evaluate the proposed transformation on existing benchmarks using a recently proposed solver for answer set programming with quantifiers, which relies on QBF solvers.

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Combining Equilibrium Logic and Dynamic Logic

Cited by 4 publications

References 13 publications

Autoepistemic equilibrium logic and epistemic specifications

Autoepistemic equilibrium logic and epistemic specifications

Logics of knowledge and action: critical analysis and challenges

Evaluating Epistemic Logic Programs via Answer Set Programming with Quantifiers

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