Reasoning with quantifier expressions in natural language combines logical and
arithmetical features, transcending strict divides between qualitative and quantitative. Our …

Coalgebraic modal logic serves as a unifying framework to study a wide range of modal
logics beyond the relational realm, including probabilistic and graded logics as well as …

We consider automata and logics that allow to reason about numerical properties of
unranked trees, expressed as Presburger constraints. We characterize non-deterministic …

During the last decades, a lot of effort was put into identifying decidable fragments of first-
order logic. Such efforts gave birth, among the others, to the two-variable fragment and the …

In this paper, we axiomatize modal logic extended with the modal operator\(M\varphi\)
saying that “there are strictly more\(\varphi\)-successors than\(\lnot\varphi\)-successors”, both …

We consider the extension of with quantifiers that state that the number of elements where a
formula holds should belong to a given ultimately periodic set. We show that both …

We introduce two versions of Presburger Automata with the Büchi acceptance condition,
working over infinite, finite-branching trees. These automata, in addition to the classical …

We introduce a logical foundation to reason on tree structures with constraints on the
number of node occurrences. Related formalisms are limited to express occurrence …

A major challenge of query language design is the combination of expressivity with effective
static analyses such as query containment. In the setting of XML, documents are seen as …

We propose a modal logic in which counting modalities appear in linear inequalities. We
show that each formula can be transformed into an equivalent graph neural network (GNN) …