This paper presents the algebraic and Kripke model soundness and completeness of a logic over Boolean monoids. An additional axiom added to the logic will cause the resulting monoid models to be representable as monoids of relations. A star operator, interpreted as reflexive, transitive closure, is conservatively added to the logic. The star operator is a relative modal operator, i.e., one that...

In this paper we give perspicuous proofs of the existence of model descriptions for nite Kripke models and of Uniform Interpolation for the theories IPC, K, GL and S4Grz, using bounded bisim-ulations.

We introduce a simplified Kripke type semantics for the {→,∧, ∗, !,1}-fragment of intuitionistic linear logic, and prove a completeness theorem with respect to the semantics by using a simple and intuitive canonical model.

A. An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced in [10]. We extend the Kripke semantics of intuitionistic logic, enriching each possible Kripke state with a set of places, and show that this semantics is both sound and complete for the logic. In the semantics, resources of a distributed system are interpreted as atoms, and pl...

The paper proposes a condition for preserving the KD45n property of a Kripke model when a sequence of update models is applied to it. The paper defines the notions of a primitive update model and a semi-reflexive KD45n (or sr-KD45n) Kripke model. It proves that updating a sr-KD45n Kripke model using a primitive update model results in a sr-KD45n Kripke model, i.e., a primitive update model pres...

We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order (or partial-order) with the modal accessibility relation generalise to the requirement that the relation and its inverse be lower semi-contin...

We investigate the logical structure of intuitionistic Kripke-Platek set theory IKP , and show that first-order logic is IQC .

Product lines are now an established framework for software design. They are specified by special diagrams called feature models. For formal analysis, the latter are usually encoded by propositional theories with Boolean semantics. We discuss a major deficiency of this semantics, and show that it can be fixed by considering that a product is an instantiation process rather than its final result...

Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond-Lifschitz transformation. The primary goal of this work is to present an alternative and epistemicbased characterization of stable m...