Mladen Vuković

Bisimulations between generalized Veltman models and Veltman models

Interpretability logic is an extension of provability logic. Veltman models and generalized Veltman models are two semantics for interpretability logic. We consider a connection between Veltman semantics and generalized Veltman semantics. We prove that for a complete image-finite generalized Veltman modelW there is a Veltman model W ′ that is bisimular to W. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Filtrations of generalized Veltman models

The filtration method is often used to prove the finite model property of modal logics. We adapt this technique to the generalized Veltman semantics for interpretability logics. In order to preserve the defining properties of generalized Veltman models, we use bisimulations to define adequate filtrations. We give an alternative proof of the finite model property of interpretability logic IL with respect to Veltman models, and we prove the finite model property of the systems ILM and ILM0 with respect to generalized Veltman models.

A bisimulation characterization for interpretability logic

A first–order formula is equivalent to the standard first–order translation of some formula of interpretability logic with respect to Veltman models if and only if it is invariant under bisimulations between Veltman models. To prove this, we use bisimulation games on Veltman models for interpretability logic. We provide characteristic formulas which formalize the existence of winning strategies in finite bisimulation games.

Some characterization and preservation theorems in modal logic

Abstract A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable . The notion of modal definability is then generalized by combining these two. For thus obtained types of modal definability on the level of Kripke models, we give characterization theorems in the usual form, in terms of algebraic closure conditions. As some consequences of these, various preservation results are presented. Also, some characterizations are strengthened by replacing closure under ultraproducts with closure under ultrapowers.

BISIMULATION QUOTIENTS OF VELTMAN MODELS

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Godel–Lob). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability l

Complexity of the interpretability logic IL

We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the length of a given formula. The existence of such algorithm, together with the previously known PSPACE hardness of the closed fragment of IL, implies PSPACE-completeness.

A new MSc curriculum in computer science and mathematics at the university of Zagreb

A new graduate curriculum in computer science and mathematics is presented. The curriculum is offered by the Department of Mathematics, University of Zagreb, and it provides students with competence in mathematics, computer science and software engineering. The emphasis is on mathematical theory relevant for computing and software, on long-term knowledge and on abstract approaches to problem solving. The teaching and assessment methods are compatible with the Bologna declaration