A Characterization of the Intuitionistic Propositional Logic

A (nother) characterization of intuitionistic propositional logic

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...

A refined calculus for Intuitionistic Propositional Logic

Since 1993, when Hudelmaier developed a O(n logn)-space decision procedure for propositional intuitionistic logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. This has been done working on proof-search strategies and on implementation structures more than on logical properties of the calculi. In this paper we provide a tableau calculus using the...

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...