Uniform description of calculi for all t-norm logics
Stefano Aguzzoli · 2004
A t-norm logic L/sub */ is the logic of a standard algebra [0, 1]* = ([0, 1], /sup */, /spl rarr/*, 0), for * being a continuous t-norm and /spl rarr/* its residuum. The notion of canonical t-algebra introduced by Hanikova (Neural Network World, vol.12, p.453-460, 2002) and Esteva-Godo-Montagna (Equational characterization of the subvarieties of BL generated by t-norm algebras), the sets-as-signs approach to many-valued tableau systems by Hahnle (Automated Deduction in Multiple-Valued Logics, Oxford University Press, Oxford, 1994), and finite-valued reduction techniques (S. Aguzzoli et al., Journal of Logic, Language and Information, vol.9, p.5-29, 2000; and S. Aguzzoli et al., Archive for Mathematical Logic, vol.41, p.361-399, 2002) allow us to describe in a uniform way co-NP calculi for all t-norm logics.