We investigate the problem of finding optimal axiomatizations for operators and distribution quantifiers in finitely-valued first-order logics. We show that the problem can be viewed as the minimization of certain two-valued prepositional formulas. We outline a general procedure leading to optimized quantifier rules for the sequent calculus, for natural deduction and for clause formation. In the case of operators and quantifiers based on semi-lattices, rules with a minimal branching degree can be obtained by instantiating a schema, which can also be used for optimal tableaux with sets-as-signs.
CITATION STYLE
Salzer, G. (1996). Optimal axiomatizations for multiple-valued operators and quantifiers based on semi-lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1104, pp. 688–702). Springer Verlag. https://doi.org/10.1007/3-540-61511-3_122
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