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Intuitionistic Predicate Logic with Decidable Propositional Formulas

Sakharov A.

Reports on Mathematical Logic

2007

No. 42

153-168

First-order intuitionistic logic extended with the assumption about decidability of all propositional atoms combines classical and intuitionistic properties. Two classes of formulas on which this extension coincides with classical and intuitionis tic logic, respectively, are identied. Constrained Kripke structures are introduced for modeling intuitionistic logic with decidable propositional atoms. The extent of applicability of classicalonly laws, the extent of the disjunction and existence properties, decidability issues, and translations are investigated.