The project helps coordinate and support the activities of the Croatian group which carries out research in mathematical logic and theoretical computer science. The envisioned topics of research are computability in analysis and topology, and the decidability and complexity of various logics.
We investigate several aspects of computable analysis. In particular, we examine conditions under which a semicomputable set in a computable metric or topological space is computable. Topology plays an important role in the description of such conditions. We intend to deepen the understanding of the relationship between computability and topology. We also investigate properties of computability structures on metric spaces, as well as the relationship between separable and maximal computability structures. We also examine, from the computability viewpoint, some properties of metric spaces on which a certain geometric structure is given.
Interpretability logics are extensions of provability logic GL ("Gödel-Löb"). The main open question in the area is to determine the axiomatization of the logic IL(All), i.e. the interpretability logic that is in the intersection of all the systems. In an attempt to answer this famous question, various extensions of the basic system IL are defined. We study the completeness of some extensions with respect to generalized Veltman semantics. We also study decidability and complexity, and we'd like to implementat algorithms for deciding provability. Particular consideration will be given to the complexity of description logics associated with the extensions of the propositional dynamic logic, and applied in modern knowledge base systems.
- Zvonko Iljazović (project leader)
- Vedran Čačić
- Luka Mikec
- Mladen Vuković
- Tin Perkov
- Konrad Burnik
- Lucija Validžić
- Marko Horvat
- Sebastijan Horvat
- Bojan Pažek
- Domagoj Vrgoč
- Matea Jelić
- Matea Čelar
- Tihana Strmečki