Taming Logics Szabolcs Mikulás 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.