Related papers: On Rational Closure in Description Logics of Typic…

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…

Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…

Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple…

We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…

In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the…

We study the problem of fitting a description logic (DL) ontology to a given set of positive and negative examples that take the form of an ABox and a Boolean query. While previous work has investigated this problem for the expressive DLs…

Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…

This works is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta- modelling. For this, we introduce the Description Logic ALCQM which is obtained from ALCQ by adding…

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…

The inexpressive Description Logic (DL) $\mathcal{FL}_0$, which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in $\mathcal{FL}_0$ w.r.t. general TBoxes is…

We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…

We present a new approach to integrating deep learning with knowledge-based systems that we believe shows promise. Our approach seeks to emulate reasoning structure, which can be inspected part-way through, rather than simply learning…

This thesis studies the model theoretic properties of the Description Logics (DLs) ALC, ALCI, ALCQ, as well as ALCO, ALCQO, ALCQIO and EL. TBoxes of ALC, ALCI and ALCQ are characterised as fragments of FO which are invariant under global…

While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

Recently, the description logic LE-ALC was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic. In this paper, we…

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…

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…

In this paper we consider the most common ABox reasoning services for the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short) and prove their…

The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…