Formal reasoning and semantics (FORMALS) is a research project funded by Croatian Science Foundation (HRZZ) for a period of 5 years, starting from December 1st, 2017.
Summary of the project
A new research group in mathematical logic will be established, with the aim of collaboration between researchers whose previous results were mainly in pure logic and those who previously focused on applications. An obstacle to this communication is the narrow specialization of researchers, which is very often an inevitable consequence of rapid development and the advancement of scientific disciplines. Therefore the emphasis of the project is on mutual communication and dissemination, and training of doctoral students who will be encouraged to develop this interdisciplinary approach from the very beginning of their career.
The goal of the project is mutual enrichment of pure and applied logic, with emphasis on applications of logic in computer science, and vice versa, the application of computational tools in logical and mathematical research. Another goal is to apply logic to specific problems of linguistics or, more generally, cognitive and information sciences, as well as interdisciplinary areas in which economics and mathematics overlap (game theory, social choice theory). Even though logic is at the first glance a formal and theoretical discipline, logic is also exceptionally applicable, and it is surprising to see applications of the same or similar formal systems, especially modal logics, in a variety of areas. Formalization brings conceptual precision, clarity and confidence. Formalization also provides new insights of the complexity of problems and allows for discovery of new issues that remain hidden in informal reasoning. For this purpose, it is useful to develop formalizations simple enough to be human-readable. Another purpose of formalization is a possibility to automatize solving a given problem and use computation to specify and verify algorithms which achieve this. For this, a formal proof itself does not need to be human-readable, but sufficient simplicity is still needed so that formalization is implementable, considering available computing resources.
The theoretical aspects of the project include:
- exploring the expressive power of formal languages by methods of model theory
- soundness and completeness, decidability and complexity of formal systems, especially modal logics
- exploring the possibilities of developing an abstract theory of formal semantics.
Application aspects are:
- development, research and formalization of mathematical models for problems of other disciplines
- development and implementation of algorithms
- detection of links between seemingly unrelated domains through related formalizations.
(Items denoted by the same number mutually correspond.)
Measurable results of the project will be research papers published in relevant international journals and presentation of research results at international conferences. Members of the research group have mainly mathematical background and work in Croatia, but interdisciplinary and international collaboration is planned.