A logic-algebraic tool for reasoning with Knowledge-Based Systems

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases speci ed by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on polynomials (on residue rings) which is used to design a new inference rule of algebro-geometric inspiration. Soundness and (refutational) completeness of the rule are proved. Some applications of the tools introduced in the paper are shown.Ministerio de Economía y Competitividad TIN2013-41086-

The Doxastic Interpretation of Team Semantics

We advance a doxastic interpretation for many of the logical connectives considered in Dependence Logic and in its extensions, and we argue that Team Semantics is a natural framework for reasoning about beliefs and belief updates

Uniform interpolation for propositional and modal team logics

In this paper we consider modal team logic, a generalization of classical modal logic in which it is possible to describe dependence phenomena between data. We prove that most known fragments of full modal team logic allow the elimination of the so called 'existential bisimulation quantifiers', where the existence of a certain set is required only modulo bisimulation (i.e. not in the model itself but possibly in a bisimilar model). As a consequence, we prove that these fragments enjoy the uniform interpolation property