Related papers: Fusions of Description Logics and Abstract Descrip…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
We show that the unification problem `is there a substitution instance of a given formula that is provable in a given logic?' is undecidable for basic modal logics K and K4 extended with the universal modality. It follows that the…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Bundled products are often offered as good deals to customers. When we bundle quantifiers and modalities together (as in $\exists x \Box$, $\Diamond \forall x$ etc.) in first-order modal logic (FOML), we get new logical operators whose…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
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,…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…
In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…