Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which is characteristic of common-sense contexts. However, it is not easy for a modeller to choose among these systems the one that better fits its domain from an ontological point of view. In this paper we first propose a framework based on the notions of exceptionality and defeasibility in order to be able to compare formalisms and reveal their ontological commitments. Then, we apply this framework to compare four systems, showing the differences that may occur from an ontological perspective.

Abstract Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in , that is, the language underlying OWL QL. We provide a definition for knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in with defeasible axioms.1

Abstract Dealing with context-dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies, due to nontrivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables, for example, reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.

The problem of reasoning with context dependent knowledge has recently gained interest in the area of description logic-based knowledge bases (KBs). Among the several proposals, we consider the Contextualized Knowledge Repository (CKR) framework. The CKR model has been recently extended with the capability of reasoning with global (context independent) defeasible axioms that can be overridden by local (context specific) knowledge. In CKR applications it is often useful to reason over a hierarchical organization of contexts. We highlight here our recent efforts on extending the CKR framework to allow for the representation of exception handling in the inheritance of knowledge across local contexts. We first concentrated on a limitation to a particular kind of context organization, i.e., ranked hierarchies, which allows us to simplify the definition of reasoning procedures. We then further generalized the proposal to extend the reasoning on exception handling over general contextual hierarchies. In this paper we summarize the basic definitions for simple CKRs with Justifiable Exceptions, the emerging computational properties, and the ASP-based reasoning procedures that we developed. Moreover, we highlight the open challenges in generalizing the approach and our future directions.

The Contextualized Knowledge Repository (CKR) framework was conceived as a logic-based approach for representing context dependent knowledge, which is a well-known area of study in AI. The framework has a two-layer structure with a global context that contains context-independent knowledge and meta-information about the contexts, and a set of local contexts with specific knowledge bases. In many practical cases, it is desirable that inherited global knowledge can be "overridden" at the local level. In order to address this need, we present an extension of CKR with global defeasible axioms: these axioms locally apply to (tuples of) individuals unless an exception for overriding exists; such an exception, however, requires a justification that is provable from the knowledge base. We formalize this intuition and study its semantic and computational properties. Furthermore, we present a translation of extended CKRs to datalog programs under the answer set (i.e., stable) semantics and we present an implementation prototype. Our work adds to the body of results on using deductive database technology in these areas, and provides an expressive formalism for exception handling by overriding.

Constructive description logics define interpretations of description logics under different constructive semantics. These logics have been mostly studied from the point of view of their formal properties: limited practical approaches have been shown for their use in knowledge representation and Se mantic Web languages and tools (which, on the other hand, constitute the distinctive applications of description logics). In this paper we demonstrate a solution to address this aspect: from the theoretical point of view, we first introduce an information terms semantics for the minimal description logic ɛℒ and we establish formal results linking this constructive semantics to answer set semantics. Using these results, on the practical side, we then present a prototype managing one aspect of such semantics (the generation of information terms of a knowledge base) using OWL-EL ontologies and “off the shelf” tools.

As the amount of available linked data expand and the number of related applications increases, the management of aspects such as provenance and access control of such data begin to become an issue. Current approaches do not provide sufficient support for automatic reasoning over different metadata types and their possible interdependencies. MetaReasons is a framework that supports representation and automated reasoning over metadata in a single logical formalism. Different types of metadata, like data-provenance and accessibility-restrictions, are represented as distinct meta-theories and dependencies between metadata types are represented by rules between different meta-theories. In this paper we present the definition of the MetaReasons framework and two examples meta-theories for provenance and access control. Moreover, we propose a materialization calculus for forward reasoning on the two aspects.

The capability of dealing with context sensitive knowledge is recognized as a crucial aspect in the management of massive amounts of Semantic Web (SW) data. Contextual knowledge can be modelled either by adopting the primitives from RDF/OWL based SW languages or by extending such languages with new specific constructs for context representation. In this paper, we show the benefits of the context-based solution by comparing modelling and reasoning in the two approaches on the paradigmatic use case of FIFA World Cup. The comparison considers the three key aspects of engineering and exploiting knowledge: (i) simplicity and expressivity of the (formal) language; (ii) compactness of the representation; and (iii) efficiency of reasoning. As for (i), we show that the context-based language enables the construction of simpler and more intuitive models while the RDF/OWL "flat" model presents practical limitations in modelling cross-contextual knowledge. For (ii), we show that the contextualized model is more compact than the OWL based model. Finally for (iii), query answering in the context-based model outperforms in most of the cases performances on the flat model.

Following the approaches given in recent works about action languages over description logics, we propose an action formalism based on a constructive information terms semantics for ALC. We discuss how a notion of state can be naturally encoded by this semantics. We address the problems of determining executability of an action, building the state obtained by an action application and checking its consistency: we present an algorithm to solve the latter two problems.