Formal systems and modeling (FORMALS-2) is a research project funded by Croatian Science Foundation (HRZZ), grant IP-2024-05-3882, for a period of 3 years, starting from December 9th, 2024.
The project coordinates the work of a research group in mathematical logic and applications, formed through the previous project Formal reasoning and semantics (FORMALS, Croatian Science Foundation grant UIP-2017-05-9219), in which collaboration was established between researchers in pure and applied logic. Focus of the proposal are applications of logic in computer science and vice versa, applications of computational tools in logical and mathematical research, and applications of logic to problems of other fields (linguistics, cognitive and information sciences, social choice theory). Modal logic systems are of particular interest, since they are applied in surprisingly different areas in similar way. Modeling and formalization of problems brings conceptual clarity, confidence in proving new results and enlightens issues which often remain hidden in informal reasoning. Research group members have background in mathematics, information sciences and linguistics.
Project topics include:
1) modal logic
2) logical and computational aspects of social choice theory
3) applications to cyber-physical systems and cognitive-linguistic analysis
4) fundamental and interdisciplinary topics in logic and mathematics
Objectives include:
1) completeness, decidability and complexity of modal logic systems, relations between different semantics of interpretability logic
2) axiomatization and formalization of the notion of compromise
3) developing methods and tools for identification of properties of language structures
4) generalization of modal semantics by means of categorial logic and topos theory
The methodology is mathematical modeling and logical formalization of given problems, deductive research of the obtained formalization and application of its results to the starting problem. When appropriate, algorithms to solve given problems will be developed and implemented. Measurable results of the project will be research papers published in relevant international journals and presented at competitive international conferences. These results will be listed below. The results of the previous project are listed here.
