Related papers: Description Logics with Two Types of Definite Desc…
We study bisimulations for useful description logics. The simplest among the considered logics is $\mathcal{ALC}_{reg}$ (a variant of PDL). The others extend that logic with inverse roles, nominals, quantified number restrictions, the…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…
We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DL-Lite and EL. Our characterizations are relative to first-order logic, based on a wide range…
The quest for acquiring a formal representation of the knowledge of a domain of interest has attracted researchers with various backgrounds into a diverse field called ontology learning. We highlight classical machine learning and data…
We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e.,…
Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the…
Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
In this paper, we study computational complexity and expressive power of modal operators for definite descriptions, which correspond to statements `the modal world which satisfies formula \(varphi\)'. We show that adding such operators to…
Ontologies are a popular way of representing domain knowledge, in particular, knowledge in domains related to life sciences. (Semi-)automating the process of building an ontology has attracted researchers from different communities into a…
We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…