Terminating Tableaux for Graded Hybrid Logic with Global Modalities and Role Hierarchies

Abstract

We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through pattern-based blocking. Previous approaches to related logics all rely on chain-based blocking. Besides being conceptually simple and suitable for efficient implementation, the pattern-based approach gives us a NExpTime complexity bound for the decision procedure.

Keywords

• computer science - logic in computer science
• f.4.1, i.2.3, i.2.4