A Method of Generating Modal Logics Defining Jaśkowski’s Discussive D2 Consequence

Nasieniewski, Marek; Pietruszczak, Andrzej

doi:10.1007/978-94-017-9011-6_6

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…Proof. We show that D ⊆ D. First, by the standard formulation of D and (rn) we see that Ω ⊆ D-it is enough to use necessitation for respective axioms of D. Besides by (8), D is closed on (rp ⇐ ). We will prove that D is closed on ( mp − ).…”

Section: Fact 5 ([14]mentioning

confidence: 87%

“…We will prove that D is closed on ( mp − ). Assume that ϕ, (ϕ → ψ) ∈ D. By (rn), ϕ ∈ D, while by (D), we have ♦(ϕ → ψ) ∈ D hence using (3) we obtain ϕ → ♦ψ ∈ D. Thus, by modus ponens ♦ψ ∈ D and by (8), ψ ∈ D. The fact that D is closed on ( mp) follows by axiom (K) and modus ponens. Finally, D is closed on ( rn) by necessitation.…”

Section: Fact 5 ([14]mentioning

confidence: 92%

“…In various papers it has been shown (see [3][4][5][6][7]) that to be able to formulate D 2 , one can use various modal logics. (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]).…”

Section: And the Minimal Variant Of Discussive Logicmentioning

confidence: 99%

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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: Fact 5 ([14]mentioning

confidence: 87%

Section: Fact 5 ([14]mentioning

confidence: 92%

Section: And the Minimal Variant Of Discussive Logicmentioning

confidence: 99%

See 1 more Smart Citation

A Kotas-Style Characterisation of Minimal Discussive Logic

Mruczek-Nasieniewska

Nasieniewski

2019

Axioms

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“…algebraicstyle semantics for D 2 have been studied in [11,14,29]. Further (metalogical) properties and other issues related to Jaśkowski's logic have been presented in [26,31,32] Notably, it is known that the logic D 2 is not finite-valued ( [29]). Hence, Jaśkowski's framework essentially differs from 3-valued approach to paraconsistency.…”

Section: Non-fregean Jaśkowski's Discussive Logicmentioning

confidence: 99%

Paraconsistency in Non-Fregean Framework

Golińska-Pilarek

2024

Stud Logica

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A non-Fregean framework aims to provide a formal tool for reasoning about semantic denotations of sentences and their interactions. Extending a logic to its non-Fregean version involves introducing a new connective $$\equiv $$ ≡ that allows to separate denotations of sentences from their logical values. Intuitively, $$\equiv $$ ≡ combines two sentences $$\varphi $$ φ and $$\psi $$ ψ into a true one whenever $$\varphi $$ φ and $$\psi $$ ψ have the same semantic correlates, describe the same situations, or have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk’s logics (Logic of Descriptions $$\textsf{LD}$$ LD , Logic of Descriptions with Suszko’s Axioms $$\textsf{LDS}$$ LDS , Logic of Equimeaning $$\textsf{LDE}$$ LDE ) with non-Fregean versions of certain well-known paraconsistent logics (Jaśkowski’s Discussive Logic $$\textsf{D}_2$$ D 2 , Logic of Paradox $$\textsf{LP}$$ LP , Logics of Formal Inconsistency $$\textsf{LFI}{1}$$ LFI 1 and $$\textsf{LFI}{2}$$ LFI 2 ). We prove that Grzegorczyk’s logics are either weaker than or incomparable to non-Fregean extensions of $$\textsf{LP}$$ LP , $$\textsf{LFI}{1}$$ LFI 1 , $$\textsf{LFI}{2}$$ LFI 2 . Furthermore, we show that non-Fregean extensions of $$\textsf{LP}$$ LP , $$\textsf{LFI}{1}$$ LFI 1 , $$\textsf{LFI}{2}$$ LFI 2 , and $$\textsf{D}_2$$ D 2 are more expressive than their original counterparts. Our results highlight that the non-Fregean connective $$\equiv $$ ≡ can serve as a tool for expressing various properties of the ontology underlying the logics under consideration.

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Coping with Inconsistencies in Legal Reasoning

Urchs

2021

New Developments in Legal Reasoning and Logic

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A Method of Generating Modal Logics Defining Jaśkowski’s Discussive D2 Consequence

Cited by 3 publications

References 5 publications

A Kotas-Style Characterisation of Minimal Discussive Logic

A Kotas-Style Characterisation of Minimal Discussive Logic

Paraconsistency in Non-Fregean Framework

Coping with Inconsistencies in Legal Reasoning

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