Optimal Axiomatizations of Finitely Valued Logics

Gernot Salzer
2000 Information and Computation  
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 propositional formulas. We outline a general procedure leading to optimized operator and quantifier rules for the sequent calculus, for natural deduction, and for clause formation. The main tools are variants of two-valued and many-valued propositional resolution, as well as a novel
more » ... le called combination. In the case of operators and quantifiers based on semilattices, 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.
doi:10.1006/inco.1999.2862 fatcat:r6r7p6dturbbtnfrmnlyugw53u