Belief Based on Inconsistent Information

Bílková, Marta; Frittella, Sabine; Majer, Ondrej; Nazari, Sajad

doi:10.1007/978-3-030-65840-3_5

Cited by 14 publications

(28 citation statements)

References 17 publications

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“…Lukasiewicz infinite-valued logic was first considered by Lukasiewicz and Tarski in their paper [39], published in 1930. This logic, along with its finite-valued counterparts 5 , prominently the three-valued system introduced by Lukasiewicz already in 1920 [37], sought to capture some types of uncertainty in the semantics of natural language that users have little difficulty internalizing and employing on a daily basis, but that appeared difficult to model within-in fact appeared inconsistent with-classical logic.…”

Section: Evolution Of the Three Logicsmentioning

confidence: 99%

“…6 These initial considerations developed into one of several grand avenues toward formal many-valued and fuzzy logic (with other such considerations provided by Zadeh and Goguen, Gödel, Heyting, or Post; see [26,Section 10.1]) and a fortiori also to, on the one hand, advanced theory of Lukasiewicz logic and MV-algebras-see [9,44,15] for overviews, and on the other, applications and (re-) interpretations that the formal system of fuzzy logic has to offer in the area of reasoning, broadly conceived: here we cannot aim for a complete picture, see e.g. [36,5,13] for some recent developments.…”

Section: Evolution Of the Three Logicsmentioning

confidence: 99%

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Rational Pavelka logic: the best among three worlds?

Haniková¹

2021

Preprint

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This comparative survey explores three formal approaches to reasoning with partly true statements and degrees of truth, within the family of Lukasiewicz logic. These approaches are represented by infinite-valued Lukasiewicz logic ( L), Rational Pavelka logic (RPL) and a logic with graded formulas that we refer to as Graded Rational Pavelka logic (GRPL). Truth constants for all rationals between 0 and 1 are used as a technical means to calibrate degrees of truth. Lukasiewicz logic ostensibly features no truth constants except 0 and 1; Rational Pavelka logic includes constants in the basic language, with suitable axioms; Graded Rational Pavelka logic works with graded formulas and proofs, following the original intent of Pavelka, inspired by Goguen's work. Historically, Pavelka's papers precede the definition of GRPL, which in turn precedes RPL; retrieving these steps, we discuss how these formal systems naturally evolve from each other, and we also recall how this process has been a somewhat contentious issue in the realm of Lukasiewicz logic. This work can also be read as a case study in logics, their fragments, and the relationship of the fragments to a logic.

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Section: Evolution Of the Three Logicsmentioning

confidence: 99%

Section: Evolution Of the Three Logicsmentioning

confidence: 99%

Rational Pavelka logic: the best among three worlds?

Haniková¹

2021

Preprint

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“…A broader motivation. This paper is a part of the project introduced in [6] aiming to develop a modular logical framework for reasoning based on uncertain, incomplete and inconsistent information. We model an agent who builds her beliefs based on probabilistic information aggregated from multiple sources.…”

Section: Introductionmentioning

confidence: 99%

“…Roughly speaking, the lower layer of events or evidence encodes the information given by the sources, while the upper layer encodes reasoning with the agent's belief based on this information, and the belief modalities connect the two layers. In [6], we have proposed two-layer modal logics to formalise such probabilistic reasoning in a potentially paraconsistent context.…”

Section: Introductionmentioning

confidence: 99%

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Constraint tableaux for two-dimensional fuzzy logics

Bílková,

Frittella,

Kozhemiachenko

2021

Preprint

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We introduce two-dimensional logics based on Lukasiewicz and Gödel logics to formalize paraconsitent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product of the [0, 1] interval. The first (resp. second) coordinate encodes the positive (resp. negative) information one has about a statement. We propose constraint tableaux that provide a modular framework to address their completeness and complexity.

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Intuitionistic propositional probability logic

Ilić‐Stepić¹,

Knežević²,

Ognjanović³

2022

Mathematical Logic Qtrly

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We give a sound and complete axiomatization of a probabilistic extension of intuitionistic logic. Reasoning with probability operators is also intuitionistic (in contradistinction to other works on this topic), i.e., measure functions used for modeling probability operators are partial functions. Finally, we present a decision procedure for our logic, which is a combination of linear programming and an intuitionistic tableaux method.

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Belief Based on Inconsistent Information

Cited by 14 publications

References 17 publications

Rational Pavelka logic: the best among three worlds?

Rational Pavelka logic: the best among three worlds?

Constraint tableaux for two-dimensional fuzzy logics

Intuitionistic propositional probability logic

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