Prime implicates and relevant belief revision

Putte, Frederik Van De

doi:10.1093/logcom/exr040

Cited by 10 publications

(3 citation statements)

References 9 publications

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“…Many studies focused on belief change within the framework of propositional logic fragments, particularly on belief revision [4,17,51,41,6], belief merging [7], belief update [11] and belief contraction [15,46,2,49,14,50]. However, as far as we know, research in belief contraction has been mainly devoted to the Horn fragment and belief erasure has attracted no attention.…”

Section: Introductionmentioning

confidence: 99%

Belief contraction and erasure in fragments of propositional logic

Creignou

Ktari

Papini

2022

Journal of Logic and Computation

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Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments and that the result of revision remains in the fragment under consideration. Later, this notion of refinement was generalized to belief change operators. Whereas refinement allowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction and erasure. We propose a specific notion of refinement for contraction and erasure operators, called reasonable refinement. This allows us to provide refined contraction and erasure operators that satisfy the basic postulates. We study the logical properties of reasonable refinement of two model-based contraction operators and two model-based erasure operators. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Krom and affine fragments.

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Section: Introductionmentioning

confidence: 99%

Belief contraction and erasure in fragments of propositional logic

Creignou

Ktari

Papini

2022

Journal of Logic and Computation

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“…Many studies focused on belief change within the framework of propositional logic fragments, particularly on belief contraction [2,37,14], on belief revision [4,13,38,32,6] and more recently on belief merging [7]. However, as far as we know, the problem of belief update within fragments of propositional logic has not been addressed so far, except for complexity results in the Horn case [17,30].…”

Section: Introductionmentioning

confidence: 99%

Belief Update Within Propositional Fragments

Creignou

Ktari²,

Papini³

2015

Lecture Notes in Computer Science

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Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

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“…There is an extensive literature on the theory of belief revision. [7][8][9][10] Actually, it was started with the work of Alchourrón et al 11 in 1985, which was studied from the perspective of structural properties of reasoning about believes. In recent years, some dynamic logical models of belief and knowledge have been developed.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Dynamic Belief Logic System

Jing

Luo

Zhang

2014

Int. J. Intell. Syst.

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In this paper, we develop a fuzzy dynamic belief revision logic system. In our system, propositions take truth values in a set of multiple fuzzy linguistic terms, which people use in everyday life. And we use a uninorm operator to aggregate the linguistic truth values of the same proposition but drawn from two different rules because uninorms can reflect well that the aggregated result of two somehow negative truth values of the same proposition should be more negative, the aggregated result of two somehow positive ones should be more positive, and the result of a negative one and a positive one is a compromise. In this system, the belief on a proposition is the linguistic truth of the proposition in the most possible world according to the current preference over all possible worlds. In the light of new information, the preference degrees of possible worlds will be updated. Accordingly, the most possible world will be changed to another and thus an old belief on a propositional formula will be changed to the linguistic truth of the proposition in the new most possible world. Moreover, we prove the soundness and completeness of our fuzzy dynamic belief revision system. In addition, we also prove that our belief revision method in fuzzy environment satisfies some relevant ones of standard AGM postulates (named after the names of their proponents, Alchourrón, Gärdenfors, and Makinson).

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Prime implicates and relevant belief revision

Cited by 10 publications

References 9 publications

Belief contraction and erasure in fragments of propositional logic

Belief contraction and erasure in fragments of propositional logic

Belief Update Within Propositional Fragments

A Fuzzy Dynamic Belief Logic System

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