The notion of logical consequence, under the classical tradition, is the fundamental relation between premises and conclusion in any valid piece of reasoning. In this way, the foundations of logical consequence can be seen on two main aspects: model-theoretic and proof-theoretically. There are, however, many general problems concerning both approaches, which we investigate in the present project.

Questions of combining semantics and non-classical logics give new and very promising impetus to the research about new models of computation, such as quantum computation and information, and about quantum algorithms and quantum cryptography. The impact of practical applications of combinations of logics into the fields of theorem proving, AI, belief revision, probability and possibility will continued to be studied, inheriting from the previous project (ConsRel 2004\14107-2). This amply justifies the interest in starting from the perspective of combining notions of logical consequence to investigate probabilistic, computational and philosophical topics.