The decidability of dependency in intuitionistic propositional logic

The Decidability of Dependency 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...

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...

Semantics of intuitionistic propositional logic

Intuitionistic logic is a weakening of classical logic by omitting, most prominently, the principle of excluded middle and the reductio ad absurdum rule. As a consequence, this logic has a wider range of semantical interpretations. The motivating semantics is the so called Brouwer-Heyting-Kolmogorov interpretation of logic. The propositions A,B,C, . . . are regarded as problems or tasks to be s...

Bisimulation and Propositional Intuitionistic Logic

The Brouwer-Heyting-Kolmogorov interpretation of intuition-istic logic suggests that p q can be interpreted as a computation that given a proof of p constructs a proof of q. Dually, we show that every nite canonical model of q contains a nite canonical model of p. If q and p are interderivable, their canonical models contain each other. Using this insight, we are able to characterize validity i...