I am interested in decidable fragments of First-Order Logic extended with
generalized counting quantifiers (and more general some variants of arithmetics).
I study their expressive power, complexity of satisfiability, definability
I enjoy the interplay of such logics, databases, automata theory and algebra.
I am particularly interested in logics describing properties of trees and words, such as temporal logics (LTL, CTL), XPath and logics enjoining tree model property (modal logics, description logics, guarded fragments). I've been slightly interested in algebraic approach to definability problems lately.
Project webpage: [not yet]The main goal of the project is to develop decision procedures and to study theoretical properties of logics extended with generalized counting quantifiers. Such quantifiers will formalize a numerous constructs from natural language e.g. "at most", "an even number", "every five of", "at least" or "less than 70%".