Finite-valued logics defined by generalized matrices, as opposed to those defined by standard logical matrices, are not necessarily structural, finite, ore decidable, and hence the search for formal criteria for these properties is of considerable importance. The problem of decidability of finite-valued propositional logics is examined. The concept of a computational semantics is introduced and it is shown that a finite-valued propositional logic is decidable if and only if it has a computational semantics. >