Irreflexive modality in the intuitionistic propositional logic and Novikov completeness

Journal of Philosophical Logic 28 (2):175-197 (1999)
Abstract
A. Kuznetsov considered a logic which extended intuitionistic propositional logic by adding a notion of 'irreflexive modality'. We describe an extension of Kuznetsov's logic having the following properties: (a) it is the unique maximal conservative (over intuitionistic propositional logic) extension of Kuznetsov's logic; (b) it determines a new unary logical connective w.r.t. Novikov's approach, i.e., there is no explicit expression within the system for the additional connective; (c) it is axiomatizable by means of one simple additional axiom scheme
Keywords intuitionistic logic  new connective  Novikov completeness
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Reprint years 2004
DOI 10.1023/A:1004229908345
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The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Nonstandard Connectives of Intuitionistic Propositional Logic.Michael Kaminski - 1988 - Notre Dame Journal of Formal Logic 29 (3):309-331.

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