%Nr: DS-95-12
%Author: Szabolcs Mikul\'as
%Title: Taming Logics
Abstract:
Taming amounts to finding computationally well-behaved versions of logics
and classes of algebras. The main concern of the dissertation is to find
decidable and complete versions of arrow logic and predicate logic. These
results are achieved by proving the equivalent decidability and finite
axiomatizability theorems for the corresponding classes of binary and
higher-order relations.
The connections between logics and algebras are explained in an
introductory chapter. One chapter deals with reducts of arrow logic (e.g.
Lambek calculus), another with arrow logics with extended similarity types
(difference operator, graded modalities). The last chapter provides
sufficient and necessary conditions for representability of relation and
cylindric algebras, which yield completeness results for arrow logics and
first-order logics.