A Characterisation of Some $$\mathbf {Z}$$ Z -Like Logics

Mruczek-Nasieniewska, Krystyna; Nasieniewski, Marek

doi:10.1007/s11787-018-0184-9

Cited by 4 publications

(5 citation statements)

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“…In the present paper we strengthen observations given in [10] using only impossibility connective. The smallest logic N + that we are using here, is an extension of the mentioned logic N. The new translations presented in the current paper allow directly for obtaining an extension of N + from any regular extension of the deontic logic D2.…”

Section: Introductionsupporting

confidence: 91%

“…Let us recall a class of logics considered in [10]: Definition 2. Let R∼ ∼ be the class of all logics that are non-trivial subsets of For∼ ∼ , containing the full positive classical logic in the language {∧, ∨, →}, including the following formulas:…”

Section: Logics Corresponding To Regular Extensions Of D2mentioning

confidence: 99%

“…In [10] a correspondence between elements of R∼ ∼ and regular extensions D2 was investigated. In the present paper we consider a simplified version of the class R∼ ∼ , with logics in the language with∼ as the only negation.…”

Section: Let Formentioning

confidence: 99%

“…We are using a reduct of the language with two negations (considered in [10]), so also validity and truth are meant accordingly. To keep the paper self-contained we recall these definitions.…”

Section: Semantical Correspondencementioning

confidence: 99%

“…However this could not be repeated in a unified way in the case of regular logics ( [8,9]). Thus, in [10], next to "it is possible that not" the impossibility operator was also used to obtain more general result on the mentioned expressibility, but this time of some regular logics. For discussion of various negations in the context of the natural language one can consult [12].…”

Section: Introductionmentioning

confidence: 99%

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Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

Mruczek-Nasieniewska

Nasieniewski²

2017

B Sect Log

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In [1] J.-Y. Béziau formulated a logic called Z. Béziau's idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular, it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar, but only partial results has been obtained also for regular logics (see [8] and [9]).In (Došen,[2]) a logic N has been investigated in the language with negation, implication, conjunction and disjunction by axioms of positive intuitionistic logic, the right-to-left part of the second de Morgan law, and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation (see [3, p. 300]). In the present paper we consider an extension of N denoted by N + . We will prove that every extension of N + that is closed under the same rules as N + , corresponds to a regular logic being an extension of the regular deontic logic D2 1 * The authors of this work benefited from support provided by Polish National Science Centre (NCN), grant number 2016/23/B/HS1/00344.The authors also thank the anonymous referee of the journal BSL for his/her valuable comments on the earlier version of the paper.1 Notice that 'D2' has nothing to do with notation for Jaśkowski's logic D 2 . D2 was introduced by Lemmon ([4]). 264Krystyna Mruczek-Nasieniewska and Marek Nasieniewski (see [4] and [13]). The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N + .

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Section: Introductionsupporting

confidence: 91%

Section: Logics Corresponding To Regular Extensions Of D2mentioning

confidence: 99%

Section: Let Formentioning

confidence: 99%

Section: Semantical Correspondencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

Mruczek-Nasieniewska

Nasieniewski²

2017

B Sect Log

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On Correspondence of Standard Modalities and Negative Ones on the Basis of Regular and Quasi-regular Logics

Mruczek-Nasieniewska

Nasieniewski

2020

Stud Logica

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Connexive Negation

Estrada-González,

Nicolás-Francisco

2023

Stud Logica

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Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view.

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A Characterisation of Some $$\mathbf {Z}$$ Z -Like Logics

Cited by 4 publications

References 4 publications

Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

On Correspondence of Standard Modalities and Negative Ones on the Basis of Regular and Quasi-regular Logics

Connexive Negation

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