Possibility semantics. Possibility semantics for modal logic is a generalization of standard Kripke semantics. In this semantics, a possibility frame has a refinement relation which is a partial order between states, in addition to the accessibility relation for modalities. From an algebraic perspective, full possibility frames are dually equivalent to complete Boolean algebras with complete op...

Mathematical models of complex objects in the form interval difference equations are built on basis obtained experimental data within limits inductive approach. At same time, interpretation physical properties object base such model is enough. A method transformation a mathematical differential was proposed article. The based formulas for representing values function at node grid Taylor series ...

Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their structure following a game semantics approach. Inductive types are interpreted as least fixed points, and we prove an internal completeness result giving an exp...

We define the algorithm ALBA for the language of the same distributive modal logic (DML) for which a Sahlqvist theorem was proved by Gehrke, Nagahashi, and Venema. Successful executions of ALBA compute the local first-order correspondents of input DML inequalities, and also guarantee their canonicity. The class of inequalities on which ALBA is successful is strictly larger than the newly introd...

We give a probabilistic interpretation of first-order formulas based on Valiants model of pac-learning. We study the resulting notion of probabilistic or approximate truth and take some first steps in developing its model theory. In particular we show that every fixed error parameter determining the precision of universal quantification gives rise to a different class of tautologies. Finally we...