On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus

Bochvar, D. A.; Bergmann, Merrie

doi:10.1080/01445348108837023

Cited by 225 publications

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“…Among them, only six are commutative and only five associative. These five conjunctions are already known in literature and precisely, they have been studied in the following logics: Sette (1973), Sobociński (1952), Lukasiewicz (Borowski, 1970), Kleene (1952), Bochvar (1981. In Table 1, we list all the 14 conjunctions.…”

Section: Connectives In Three-valued Logicsmentioning

confidence: 99%

A modal theorem-preserving translation of a class of three-valued logics of incomplete information

Ciucci

Dubois

2013

Journal of Applied Non-Classical Logics

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There are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified formula in a large range of three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, Lukasiewicz and Nelson logics. We show that Priest logic of paradox, closely connected to Kleene's, can also be translated into our modal setting, just exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management.

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Section: Connectives In Three-valued Logicsmentioning

confidence: 99%

A modal theorem-preserving translation of a class of three-valued logics of incomplete information

Ciucci

Dubois

2013

Journal of Applied Non-Classical Logics

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“…In order to formally capture local accommodation, we make use of the A-operator, defined as follows (Bochvar 1981;Beaver and Krahmer 2001).…”

Section: (39)mentioning

confidence: 99%

Presupposed ignorance and exhaustification: how scalar implicatures and presuppositions interact

Spector

Sudo

2017

Linguist and Philos

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We investigate the interactions between scalar implicatures and presuppositions in sentences containing both a scalar item and presupposition trigger. We first critically discuss Gajewski and Sharvit's previous approach. We then closely examine two ways of integrating an exhaustivity-based theory of scalar implicatures with a trivalent approach to presuppositions. The empirical side of our discussion focuses on two novel observations: (i) the interactions between prosody and monotonicity, and (ii) what we call presupposed ignorance. In order to account for these observations, our final proposal relies on two mechanisms of scalar strengthening, the Presupposed Ignorance Principle and an exhaustivity operator which lets the presuppositions of negated alternatives project.The authors' names are alphabetically ordered. The present work has greatly benefitted from discussions with a number of colleagues,

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“…The idea here is that negation is more complicated than it seems at first glance, much more complicated than the simple treatment of standard logic would have it. Early on, Bochvar [4] gave a treatment of the Liar which used three-valued logic to say that the Liar has the truth value "meaningless." A problem with this is that the paradox could resurface in the form of the Strengthened Liar: "This sentence is either false or meaningless."…”

Section: Bulletin (New Seriesmentioning

confidence: 99%

Book Review: The Liar: An essay in truth and circularity

Moss¹

1989

Bull. Amer. Math. Soc.

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On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus

Cited by 225 publications

References 0 publications

A modal theorem-preserving translation of a class of three-valued logics of incomplete information

A modal theorem-preserving translation of a class of three-valued logics of incomplete information

Presupposed ignorance and exhaustification: how scalar implicatures and presuppositions interact

Book Review: The Liar: An essay in truth and circularity

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