Abstract
We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable.
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Zimmermann, E. A Predicate Logical Extension of a Subintuitionistic Propositional Logic. Studia Logica 72, 401–410 (2002). https://doi.org/10.1023/A:1021897508223
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DOI: https://doi.org/10.1023/A:1021897508223