Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering

Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

A survey of large-scale reasoning on the Web of data

As more and more data is being generated by sensor networks, social media and organizations, the Webinterlinking this wealth of information becomes more complex. This is particularly true for the so-calledWeb of Data, in which data is semantically enriched and interlinked using ontologies. In this large anduncoordinated environment, reasoning can be used to check the consistency of the data and of asso-ciated ontologies, or to infer logical consequences which, in turn, can be used to obtain new insightsfrom the data. However, reasoning approaches need to be scalable in order to enable reasoning over theentire Web of Data. To address this problem, several high-performance reasoning systems, whichmainly implement distributed or parallel algorithms, have been proposed in the last few years. Thesesystems differ significantly; for instance in terms of reasoning expressivity, computational propertiessuch as completeness, or reasoning objectives. In order to provide afirst complete overview of thefield,this paper reports a systematic review of such scalable reasoning approaches over various ontologicallanguages, reporting details about the methods and over the conducted experiments. We highlight theshortcomings of these approaches and discuss some of the open problems related to performing scalablereasoning

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Derivation methods for hybrid knowledge bases with rules and ontologies

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaFirst of all, I would like to thank my advisor, José Júlio Alferes, for his incredible support. Right from the start, during the first semester of this work, when we were 2700 km apart and meeting regularly via Skype, until the end of this dissertation, he was always committed and available for discussions, even when he had lots of other urgent things to do. A really special thanks to Terrance Swift, whom acted as an advisor, helping me a lot in the second implementation, and correcting all XSB’s and CDF’s bugs. This implementation wouldn’t surely have reached such a fruitful end without his support. I would also like to thank all my colleagues and friends at FCT for the great work environment and for not letting me take myself too serious. A special thanks to my colleagues from Dresden for encouraging me to work even when there were so many other interesting things to do as an Erasmus student. I’m indebted to Luís Leal, Bárbara Soares, Jorge Soares and Cecília Calado, who kindly accepted to read a preliminary version of this report and gave me their valuable comments. For giving me working conditions and a partial financial support, I acknowledge the Departamento de Informática of the Faculdade de Ciências e Tecnologias of Universidade Nova de Lisboa. Last, but definitely not least, I would like to thank my parents and all my family for their continuous encouragement and motivation. A special thanks to Bruno for his love, support and patience

Epistemic Reasoning in OWL 2 DL

We extend the description logic SROIQ (OWL 2 DL) with the epistemic operator K and argue that unintended effects occur when imposing the semantics traditionally employed. Consequently, we identify the most expressive DL for which the traditional approach can still be adapted. For the epistemic extension of SROIQ and alike expressive DLs, we suggest a revised semantics that behaves more intuitively in these cases and coincides with the traditional semantics on less expressive DLs

On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.Comment: To appear in Theory and Practice of Logic Programmin