Proof-finding Algorithms for Classical and Subclassical Propositional Logics

Complementary Logics for Classical Propositional Languages

This note presents a simple axiomatic system by means of which exactly those sentences can be derived that are rated non-tautologous in classical propositional logic. Since the logic is decidable, there exist of course many algorithms that do the job, e.g. using semantic tableaux or refutation trees. However, a formulation in terms of axioms and rules of inference is by no means a straightforwa...

Efficient Loop-Check for Backward Proof Search in Some Non-classical Propositional Logics

A Uniform Proof Procedure for Classical and Non-Classical Logics

G. Görz & S. Hölldobler, eds. KI-96: Advances in Artificial Intelligence, LNAI 1137, pp. 307–319, c ©Springer Verlag, 1996. Abstract. We present a proof procedure for classical and non-classical logics. The proof search is based on the matrix-characterization of validity where an emphasis on paths and connections avoids redundancies occurring in sequent or tableaux calculi. Our uniform path-che...

Combining intermediate propositional logics with classical logic

In [17], we introduced a modal logic, called L, which combines intuitionistic propositional logic IPC and classical propositional logic CPC and is complete w.r.t. an algebraic semantics. However, L seems to be too weak for Kripke-style semantics. In this paper, we add positive and negative introspection and show that the resulting logic L5 has a Kripke semantics. For intermediate logics I , we ...

Categorical proof theory of classical propositional calculus

We investigate semantics for classical proof based on the sequent calculus. We show that the propositional connectives are not quite well-behaved from a traditional categorical perspective, and give a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly. Finally we explain the consequences of insisting on more familiar categorical behaviour.