Let V be a s.f.b. (strongly finitely based, see below) variety of algebras. The central result is Theorem 2 saying that the logic defined by all matrices (A, d) with d ε A ε V is finitely based iff the A ε V have 1st order definable cosets for their congruences. Theorem 3 states a similar axiomatization criterion for the logic determined by all matrices (A, εA), A ∈ V, ε a term which is constant in V. Applications are given in a series of examples.
KeywordsMathematical Logic Computational Linguistic Central Result Similar Axiomatization Axiomatization Criterion
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