Forgetting in multi-agent modal logics

Fang, Liangda; Liu, Yongmei; Ditmarsch, Hans van

doi:10.1016/j.artint.2018.08.003

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…We need some definitions first. Fang et al [13] introduced the projection operations on CFs. When a CF τ is represented as a tree, the operation τ ↓ prunes the leaves of this tree, and τ ↓l prunes the bottom l levels of the tree.…”

Section: Definition 6 ([19] Canonical Formulas)mentioning

confidence: 99%

A Model-Theoretic Approach to Belief Revision in Multi-Agent Belief Logic and Its Syntactic Characterizations

Liang,

Liu

2023

Frontiers in Artificial Intelligence and Applications

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Belief change studies how an agent modifies her beliefs on receiving new information. However, so far most research on belief change works on beliefs represented in propositional logic. There have been many works on integrating belief revision with reasoning about actions, and some works extending belief change from propositional logic to epistemic logics. In this paper, we study revision on beliefs of a third person represented with the multi-agent KD45 logic. Our formal technique is analogous to that of distance-based belief revision in propositional logic: to revise a KB by a formula, select from models of the formula those that are closest to models of the KB. To this end, a challenge is that in modal logics, a formula may have infinitely many Kripke models. To tackle this, we propose a variant of Moss’ canonical formulas called alternating canonical formulas, treat them as models for formulas, and define a notion of distance between them, based on the Hausdorff distance between two sets. We show that our revision satisfies all of the AGM postulates. To give syntactic characterizations of our revision, we make use of a normal form for KD45n called alternating cover disjunctive formulas (ACDFs). We give syntactic characterizations firstly on fragments of ACDFs called proper ACDFs and alternating cover conjunctive formulas (ACCFs), and finally on the whole ACDFs.

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Section: Definition 6 ([19] Canonical Formulas)mentioning

confidence: 99%

A Model-Theoretic Approach to Belief Revision in Multi-Agent Belief Logic and Its Syntactic Characterizations

Liang,

Liu

2023

Frontiers in Artificial Intelligence and Applications

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“…Therefore, computing forgetting results in S5 is reduced to compute the one in PL [26]. Forgetting was recently extended to multi-agent modal logics [27]. It is showed that computing forgetting results of formulas in disjunctive normal form is feasible in polynomial time [28].…”

Section: Forgettingmentioning

confidence: 99%

Computing Sufficient and Necessary Conditions in CTL: A Forgetting Approach

Feng

Acar²,

Wang³

et al. 2022

Information Sciences

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“…(b) each prime implicate of φ is equivalent to some conjunct c j ; (c) every c j is a prime implicate of φ s.t. A definition of forgetting for modal logics is defined in (French 2006) and it is further investigated in (Fang, Liu, and van Ditmarsch 2016). Definition 2.7.…”

Section: The Multi-agent Modal Logic K Nmentioning

confidence: 99%

Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability

Fang¹,

Wang

et al. 2019

AAAI

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Modal logics are primary formalisms for multi-agent systems but major reasoning tasks in such logics are intractable, which impedes applications of multi-agent modal logics such as automatic planning. One technique of tackling the intractability is to identify a fragment called a normal form of multiagent logics such that it is expressive but tractable for reasoning tasks such as entailment checking, bounded conjunction transformation and forgetting. For instance, DNF of propositional logic is tractable for these reasoning tasks. In this paper, we first introduce a notion of logical separability and then define a novel disjunctive normal form SDNF for the multiagent logic Kn, which overcomes some shortcomings of existing approaches. In particular, we show that every modal formula in Kn can be equivalently casted as a formula in SDNF, major reasoning tasks tractable in propositional DNF are also tractable in SDNF, and moreover, formulas in SDNF enjoy the property of logical separability. To demonstrate the usefulness of our approach, we apply SDNF in multi-agent epistemic planning. Finally, we extend these results to three more complex multi-agent logics Dn, K45n and KD45n.

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Forgetting in multi-agent modal logics

Cited by 8 publications

References 25 publications

A Model-Theoretic Approach to Belief Revision in Multi-Agent Belief Logic and Its Syntactic Characterizations

A Model-Theoretic Approach to Belief Revision in Multi-Agent Belief Logic and Its Syntactic Characterizations

Computing Sufficient and Necessary Conditions in CTL: A Forgetting Approach

Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability

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