First-order many-valued logics

Many-valued logics are a prominent family of non-classical logics whose intended semantics uses more than the two classical truth-values, truth/false. The study of these logics is stimulated by strong mutually beneficial connections with other mathematical disciplines such as universal algebra, topology, and model, proof, game and category theory. The achieved results have led to many interesting applications in other fields like philosophy and computer science. For the sake of higher expressive power and application potential of these logics, it is desirable to focus on the study of their fist-order predicate extensions. Even though there are numerous results in this area, a systematic theory of many-valued first-order logics is still lacking. The aim of the project is to initialize the development of this theory utilizing the complementary expertise of the Argentinian and Czech teams. In particular, we plan to focus on the study of logics with only unary predicates and their algebraic semantics, and the development of a model theory for these first-order logics.