Automated Synthesis of Tableau Calculi

TL;DR

This paper introduces an automated method for synthesizing sound, complete, and terminating tableau calculi from formal logic semantics, enabling automated reasoning and decision procedures for various logics.

Contribution

It provides a fully automated approach to generate tableau inference rules and blocking mechanisms, ensuring soundness, completeness, and termination for diverse logics.

Findings

Successfully applied to description logic with transitive roles.

Demonstrated for propositional intuitionistic logic.

Produced automated tableau decision procedures.

Abstract

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.