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Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
Fixpoints are an important ingredient in semantics, abstract interpretation and program logics. Their addition to a logic can add considerable expressive power. One general issue is how to define proof systems for such logics. Here we…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlier work that obtains Hennessy-Milner theorems as corollaries…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Biomedical ontologies contain numerous concept or role names involving negative knowledge such as lacks_part, absence_of. Such a representation with labels rather than logical constructors would not allow a reasoner to interpret lacks_part…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
We identify a subproblem of the model-checking problem for the epistemic \mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…
Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…
Metric Temporal Logic, $\mtlfull$ is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…