Nov. 23, 2023, 1:37 p.m.
The second prize in our best master's theses competition for Mateusz Urbańczyk
Another author sharing the second prize in our Przemka Kanarek competition for the best master's thesis in computer science is Mateusz Urbańczyk. Mateusz thesis was on Categorical semantics for model comparison games for description logics. It has been published at the FLoC'22 with Bartosz Bednarczyk, and the supervisor was Emanuel Kieroński.
The languages we use serve us to describe reality. An example is the sentence: "The mountain is high." But what if we eliminate the word "high"? Can we still express this property? We can say, "The mountain is not low," and going further, what if we exclude the use of "not"? Mathematicians have created certain games that allow proving that a given sentence cannot be expressed in a language. A specific example is Ehrenfeuchta-Fraisse's game for first-order logic.
Our work transforms games, which are a description and a list of steps, into concrete, algebraic objects on which mathematical operations can be performed. We tackled the task of categorical semantics for descriptive logics, which are variants of modal logic extended with additional operators, describing the game through a certain (co)monad.
