Since 1993, when Hudelmaier developed an O(n log n)-space decision procedure for propositional Intuitionistic Logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. In this paper a tableau calculus using the signs T, F and Fc with a new set of rules to treat signed formulas of the kind T((A → B) → C) is provided. The main feature of the calculus is the reduction of both the non-determinism in proof-search and the width of proofs with respect to Hudelmaier's one. These improvements have a significant influence on the performances of the implementation..
Ferrari, M., Fiorentini, C., Fiorino, G. (2009). A tableau calculus for Propositional Intuitionistic Logic with a refined treatment of nested implications. JOURNAL OF APPLIED NON-CLASSICAL LOGICS, 19(2), 149-166 [10.3166/jancl.19.149-166].
A tableau calculus for Propositional Intuitionistic Logic with a refined treatment of nested implications
FIORINO, GUIDO GIUSEPPE
2009
Abstract
Since 1993, when Hudelmaier developed an O(n log n)-space decision procedure for propositional Intuitionistic Logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. In this paper a tableau calculus using the signs T, F and Fc with a new set of rules to treat signed formulas of the kind T((A → B) → C) is provided. The main feature of the calculus is the reduction of both the non-determinism in proof-search and the width of proofs with respect to Hudelmaier's one. These improvements have a significant influence on the performances of the implementation..
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