Decidability of quantified propositional intuitionistic logic and S4 on trees

Details Decidability of quantified propositional intuitionistic logic and S4 on trees Decidability of quantified propositional intuitionistic logic and S4 on trees

2002-03-12

arxiv.org/abs/math/0203113v2

Mathematics

Logic

v2, 9 pages, corrections and additions; v1 8 pages

Scientific paper

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers \forall p, \exists p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a model structure which is upward closed. Kremer (1997) has shown that the quantified propositional intuitionistic logic H\pi+ based on the class of all partial orders is recursively isomorphic to full second-order logic. He raised the question of whether the logic resulting from restriction to trees is axiomatizable. It is shown that it is, in fact, decidable. The methods used can also be used to establish the decidability of modal S4 with propositional quantification on similar types of Kripke structures.

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