Classical propositional logic and decidability of variables in intuitionistic propositional logic

Classical propositional logic and decidability of variables in intuitionistic propositional logic

Let `c and `i denote derivability in classical and intuitionistic propositional logic, respectively. Then it is known that if `c A, then ΠV(A) `i A, where V(A) is the set of propositional variables in a formula A and ΠV = {p ∨ ¬p | p ∈ V } for a set V of propositional variables; see, for example, [1], and [4, p. 27] which was originally given in [5]. In this talk, we consider a problem: what se...

A modal logic amalgam of classical and intuitionistic propositional logic

We present a modal extension of classical propositional logic in which intuitionistic propositional logic is mirrored by means of the modal operator. In this sense, the modal extension combines classical and intuitionistic propositional logic avoiding the collapsing problem. Adopting ideas from a recent paper (S. Lewitzka, A denotational semantics for a Lewis-style modal system close to S1, 201...

Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers ∀p, ∃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, i.e., if h ∈ P , then h ∈ P for all h ≤ h. For propositional intuitionistic logic H, several classes of model structures are known...

The Decidability of Dependency in Intuitionistic Propositional Logic

Deciding Intuitionistic Propositional Logic via Translation into Classical Logic

W. McCune, ed. 14 International Conference on Automated Deduction (CADE-14), LNAI 1249, pp. 131–145, c ©Springer Verlag, 1997. Abstract. We present a technique that efficiently translates propositional intuitionistic formulas into propositional classical formulas. This technique allows the use of arbitrary classical theorem provers for deciding the intuitionistic validity of a given proposition...