A Kripke model K is a submodel of another Kripke modelM if K is ob tained by restricting the set of nodes ofM In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas This result is an analogue of the Lo s Tarski theorem for the Classical Predicate Calculus In appe...

Given the “possible worlds” interpretation of modal logic, a refinement of a Kripke model is another Kripke model in which an agent has ruled out some possible worlds to be consistent with some new information. The refinements of a finite Kripke model have been shown to correspond to the results of applying arbitrary action models to the Kripke model [10]. Refinement modal logics add quantifier...

We show how to generate multi-agent Kripke models from message exchanges. With these models we can analyze the epistemic consequences of a message exchange. One novelty in this approach is that we include the messages in our logical language. This allows us to model messages that mention other messages and agents that reason about messages. Our framework can be used to model a wide range of dif...

Algebraic work [9] shows that the deep theory of possible world semantics is available in the more general setting of substructural logics, at least in an algebraic guise. The question is whether it is also available in a relational form. This article seeks to set the stage for answering this question. Guided by the algebraic theory, but purely relationally we introduce a new type of frames. Th...

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

In their 1936 seminal paper, Birkhoff and von Neumann made the proposal of a non-classical logic for quantum mechanics founded on the basic lattice-order properties of all closed subspaces of a Hilbert space. These lattice-order properties are captured in the orthomodular lattice structure, characterized by a weak form of distributivity called orthomodular law. This “weak distributivity”, which...