We discuss results on global definability in basic modal logic, and contrast our model-theoretic results and proof techniques with known results about local definability.

We present an algorithmically efficient criterion of modal definability for first-order existential conjunctive formulas with several free variables. Then we apply it to establish modal definability of some family of first-order ∀∃-formulas. Finally, we use our definability results to show that, in any expressive description logic, the problem of answering modally definable conjunctive queries ...

This paper is meant to be a comment on Beth's definability theorem. In it we shall make the following points. Implicit definability as mentioned in Beth's theorem for first-order logic is a special case of a more general notion of uniqueness. If a is a nonlogical constant, Tat a set of sentences, cx* an additional constant of the same syntactical category as a and T7t* a copy of Tat with cx* in...

We study two notions of definability for classes of relational structures based on modal extensions of Łukasiewicz finitely-valued logics. The main results of the paper are the equivalent of the Goldblatt Thomason theorem for these notions of definability.