Automated Synthesis of Tableau Calculi

Details Automated Synthesis of Tableau Calculi Automated Synthesis of Tableau Calculi

2011-04-20

arxiv.org/abs/1104.4131v4

LMCS 7 (2:6) 2011

Computer Science

Logic in Computer Science

32 pages

Scientific paper

10.2168/LMCS-7(2:6)2011

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.

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