Related papers: Description logics as polyadic modal logics
This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations…
We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard…
We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…
The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices,…
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…
A categorical approach to study model comparison games in terms of comonads was recently initiated by Abramsky et al. In this work, we analyse games that appear naturally in the context of description logics and supplement them with…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Plo\v{s}\v{c}ica. The standard representations of complete ortholattices and complete perfect Heyting…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
In this paper we use display calculus to show the decidability for normal modal logic K and some of its extensions.