The use of the universal and existential quantifiers with the capability to express the concept of at least k or all but k, for a nonnegative integer k, has been thoroughly studied in various kinds of logics. In classical logic there are counting quantifiers, in modal logics graded modalities, in description logics number restrictions. Recently, the complexity issues related to the decidability...

We study the problem of satisfiability of Boolean formulas φ in conjunctive normal form whose literals have the form v ∈ S and express the membership of values to sets S of a given set system S. We establish the following dichotomy result. We show that checking the satisfiability of such formulas (called S-formulas) with three or more literals per clause is NP-complete except the trivial case w...

Logic-based argumentation offers an approach to querying and revising multiple ontologies that are inconsistent or incoherent. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉 where Φ is a minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claimα. Using dialogue games, agents (each with its own ontology) can exchange arguments an...

In this paper we present a fully symbolic TCTL model checking algorithm for incomplete timed systems. Our algorithm is able to prove that a TCTL property is violated or satisfied regardless of the implementation of unknown timed components in the system. For that purpose the algorithm computes overapproximations of sets of states fulfilling a TCTL property φ for at least one implementation of t...

We study the fixed-parameter complexity of model checking temporal logics on concurrent systems that are modeled as the product of finite systems and where the size of the formula is the parameter. We distinguish between asynchronous product and synchronous product. Sometimes it is possible to show that there is an algorithm for this with running time ( ∑ i |Ti|) O(1) · f(|φ|), where the Ti are...