On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Blondeel, Marjon; Flaminio, Tommaso; Schockaert, Steven; Godo, Lluı́s; Cock, Martine De

doi:10.1016/j.fss.2015.02.018

Cited by 8 publications

(10 citation statements)

References 20 publications

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“…Proof. Observe that (4) implies (3), and that (3) implies (2). Soundness is simple to check in general for the |= l PK case, so (1) implies (4).…”

Section: Lemma 49mentioning

confidence: 99%

“…A logic L for which there exists a set of formulas Δ(x,y) that satisfies any of the two previous equivalent properties is said to be equivalential with congruence formulas Δ(x,y). 3…”

Section: Lemma 22mentioning

confidence: 99%

“…For instance, [14][15][16] present results concerning different modal extensions of Gödel fuzzy logic, [2] is a systematic study of modal logics over finite residuated lattices and [30] deals with modal extensions of both infinitely and finitelyvalued Łukasiewicz logics. On the other hand, for instance, finitely-valued modal Łukasiewicz logics have been considered in [3] to provide formal grounds for fuzzy autoepistemic logic and certain logics of belief.…”

Section: Introductionmentioning

confidence: 99%

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On modal extensions of Product fuzzy logic

Vidal¹,

Esteva²,

Godo³

2015

J Logic Computation

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In this article, we study modal extensions of Product fuzzy logic with both algebraic semantics and relational semantics based on Kripke structures with crisp accessibility relations, when the underlying product fuzzy logic is expanded with truthconstants, the Δ operator and with two infinitary inference rules. We provide completeness results for both kinds of semantics. Finally, we also consider a generalization of possibilistic logic evaluated over product algebras.

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“…Proof. Observe that (4) implies (3), and that (3) implies (2). Soundness is simple to check in general for the |= l PK case, so (1) implies (4).…”

Section: Lemma 49mentioning

confidence: 99%

“…A logic L for which there exists a set of formulas Δ(x,y) that satisfies any of the two previous equivalent properties is said to be equivalential with congruence formulas Δ(x,y). 3…”

Section: Lemma 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On modal extensions of Product fuzzy logic

Vidal¹,

Esteva²,

Godo³

2015

J Logic Computation

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“…Moreover, in most of the literature on fuzzy modal logic, they use many‐valued logic to handle the fuzzy environment, whereas our work in this paper is based on a new method to depict the fuzziness, i.e., the linguistic truth term set, which is closer to our daily languages. In addition, the work of Blondeel et al . introduces a Hilbert‐style axiomatisation of fuzzy modal logics for belief based on finite‐valued Lukasiewicz logic and provides possible world semantics for a fuzzy autoepistemic logic.…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, in most of the literature on fuzzy modal logic, they use many-valued logic to handle the fuzzy environment, whereas our work in this paper is based on a new method to depict the fuzziness, i.e., the linguistic truth term set, which is closer to our daily languages. In addition, the work of Blondeel et al 50 introduces a Hilbert-style axiomatisation of fuzzy modal logics for belief based on finite-valued Lukasiewicz logic and provides possible world semantics for a fuzzy autoepistemic logic. In the work of Blondeel et al, 50 they model belief based on fuzzy propositions, in the sense of admitting partial degrees of truth between 0 (fully false) an 1 (fully true), whereas in our system we adopt the linguistic truth term set, which is more natural.…”

Section: Related Workmentioning

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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