On the Role of Adjunction in Para(in)consistent Logic

Urchs, Max

doi:10.1201/9780203910139.ch25

Cited by 3 publications

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“…(Jaśkowski's logic was meant to be a basis for a consequence relation and also in this case there can be given other systems than S5 which also allow to express D 2 -consequence relation (see [8]). ) Moreover, one can introduce a general discussive consequence relation framework, in which D 2 would be the set of theses of one of its special cases (for details see [9]). However, this does not mean that any modal logic would be equally good to obtain D 2 .…”

Section: And the Minimal Variant Of Discussive Logicmentioning

confidence: 99%

A Kotas-Style Characterisation of Minimal Discussive Logic

Mruczek-Nasieniewska

Nasieniewski

2019

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In this paper, we discuss a version of discussive logic determined by a certain variant of Jaśkowski’s original model of discussion. The obtained system can be treated as the minimal discussive logic. It is determined by frames with serial accessibility relation. As the smallest one, this logic can be treated as a basis which could be extended to richer discussive logics that are obtained by varying accessibility relation and resulting in a lattice of discussive logics. One has to remember that while formulating discussive logics there is no one-to-one determination of discussive logics by modal logics. For example, it is proved that Jaśkowski’s logic D 2 can be expressed by other than S 5 modal logics. In this paper we consider a deductive system for the sketchily described minimal logic. While formulating the deductive system, we apply a method of Kotas that was used to axiomatize D 2 . The obtained system determines a logic D 0 as a set of theses that is contained in D 2 . Moreover, any discussive logic that would be expressed by means of the provided model of discussion would contain D 0 , so it is the smallest discussive logic.

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Section: And the Minimal Variant Of Discussive Logicmentioning

confidence: 99%

A Kotas-Style Characterisation of Minimal Discussive Logic

Mruczek-Nasieniewska

Nasieniewski

2019

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“…One old example of non‐adjunctive propositional logical calculus is Jaskowski’s discussive logic (see Jaskowski 1948, and later developments by da Costa and Dubikajtis 1968; Kotas and da Costa 1979; Urchs 1995 and 2002). Its intuitive motivation is to refer the rise of contradictions to dialogues in which participants can contradict each other.…”

Section: Non‐adjunctive Approaches and The Italics Argumentmentioning

confidence: 99%

Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist?s Dilemma

Berto

2007

Dialectica

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In his famous work on vagueness, Russell named 'fallacy of verbalism' the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories -the non-adjunctive and relevant approaches -, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of 'intuitive reading' is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense -therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth , and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency -and this could be a welcome result for a dialetheist.

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In what sense is Kantian principle of contradiction non-classical?

Kovač

2008

LLP

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Abstract. On the ground of Kant's reformulation of the principle of contradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, ¬(φ ∧ ¬φ), φ → (¬φ → ψ), and φ ∨ ¬φ are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {φ, ¬φ} (the deduction theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order modal logic M. The quantification in M is combined with a "subject abstraction" device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski's discussive logic), relativizing state of affairs with respect to conditions such as time.

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On the Role of Adjunction in Para(in)consistent Logic

Cited by 3 publications

References 0 publications

A Kotas-Style Characterisation of Minimal Discussive Logic

A Kotas-Style Characterisation of Minimal Discussive Logic

Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist?s Dilemma

In what sense is Kantian principle of contradiction non-classical?

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