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dc.contributor.authorMruczek-Nasieniewska, Krystyna
dc.contributor.authorNasieniewski, Marek
dc.date.accessioned2018-06-22T13:54:33Z
dc.date.available2018-06-22T13:54:33Z
dc.date.issued2017
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/25180
dc.description.abstractIn [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’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 D21 (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+.en_GB
dc.language.isoenen_GB
dc.publisherWydawnictwo Uniwersytetu Łódzkiegoen_GB
dc.relation.ispartofseriesBulletin of the Section of Logic;3/4
dc.subjectnon-classical negationen_GB
dc.subjectmodalized negationen_GB
dc.subjectimpossibilityen_GB
dc.subjectcorrespondenceen_GB
dc.subjectregular modal logicsen_GB
dc.subjectthe smallest regular deontic logic D2en_GB
dc.titleLogics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2en_GB
dc.typeArticleen_GB
dc.rights.holder© Copyright by Authors, Łódź 2017; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2017en_GB
dc.page.number263–282
dc.contributor.authorAffiliationNicolaus Copernicus University in Toruń
dc.identifier.eissn2449-836X
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dc.referencesK. Mruczek-Nasieniewska and M. Nasieniewski, A Segerberg-like connection between certain classes of propositional logics, Bulletin of the Section of Logic 42 (1/2) (2013), pp. 43–52.en_GB
dc.referencesK. Mruczek-Nasieniewska and M. Nasieniewski, A Characterisation of Some Z-Like Logics, Logica Universalis, 13 pp. Online: https://link.springer.com/article/10.1007%2Fs11787-018-0184-9. DOI: https://doi.org/10.1007/s11787-018-0184-9.en_GB
dc.referencesA. Palmigiano, S. Sourabh and Z. Zhao, Sahlqvist theory for impossible worlds, Journal of Logic and Computation 27 (3) (2017), pp. 775–816, DOI: https://doi.org/10.1093/logcom/exw014.en_GB
dc.referencesD. W. Ripley, Negation in Natural Language, PhD Dissertation, University of North Carolina, 2009.en_GB
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dc.contributor.authorEmailmruczek@umk.pl
dc.contributor.authorEmailmnasien@umk.pl
dc.identifier.doi10.18778/0138-0680.46.3.4.06
dc.relation.volume46en_GB


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