Automatic Generation of Proof Tactics for Finite-Valued Logics

A number of flexible tactic-based logical frameworks are now adays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful systems resides in their responsiveness to extensibility of their reasoning capabilities, being designed o ver rule-based programming languages that allow the user to build her own ‘programs to construct proofs’ — the so-called proof tactics. The present contribution discusses the implementation of an algorithm that generates sound and complete tableau systems for a very inclusive class of suffic iently expressive finite-valued propositional logics, and then illustrates some of the challenges a nd difficulties related to the algorithmic formation of automated theorem proving tactics for such logics. The procedure on whose implementation we will report is based on a generalized notion of analyticity of proof systems that is intended to guarantee termination of the corresponding automated tactics on what concerns theoremhood in our targeted logics.