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. | |||||||||
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