4-Valued Semantics Under the OWA: A Deductive Database Approach

International Joint Conference on Artificial Intelligence, 2015

The concept of incoherence naturally arises in ontological settings, specially when integrating knowledge. In this work we study a notion of incoherence for Datalog ± ontologies based on the definition of satisfiability of a set of existential rules regarding the set of integrity constraints in a Datalog ± ontology. We show how classical inconsistency-tolerant semantics for query answering behaves when dealing with atoms that are relevant to unsatisfiable sets of existential rules, which may hamper the quality of answers-even under inconsistency-tolerant semantics, which is expected as they were not designed to confront such issues. Finally, we propose a notion of incoherency-tolerant semantics for query answering in Datalog ± , and present a particular one based on the transformation of classic Datalog ± ontologies into defeasible Datalog ± ones, which use argumentation as its reasoning machinery.

Annals of Mathematics and Artificial Intelligence, 2016

The concept of incoherence naturally arises in ontological settings, specially when integrating knowledge. In this work we study a notion of incoherence for Datalog ± ontologies based on the definition of satisfiability of a set of existential rules regarding the set of integrity constraints in a Datalog ± ontology. We show how classical inconsistency-tolerant semantics for query answering behaves when dealing with atoms that are relevant to unsatisfiable sets of existential rules, which may hamper the quality of answers-even under inconsistency-tolerant semantics, which is expected as they were not designed to confront such issues. Finally, we propose a notion of incoherency-tolerant semantics for query answering in Datalog ± , and present a particular one based on the transformation of classic Datalog ± ontologies into defeasible Datalog ± ones, which use argumentation as its reasoning machinery.

Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems, 2013

The Datalog ± family of expressive extensions of Datalog has recently been introduced as a new paradigm for query answering over ontologies, which captures and extends several common description logics. It extends plain Datalog by features such as existentially quantified rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and tractability. In this paper, we continue the research on Datalog ±. More precisely, we generalize the well-founded semantics (WFS), as the standard semantics for nonmonotonic normal programs in the database context, to Datalog ± programs with negation under the unique name assumption (UNA). We prove that for guarded Datalog ± with negation under the standard WFS, answering normal Boolean conjunctive queries is decidable, and we provide precise complexity results for this problem, namely, in particular, completeness for PTIME (resp., 2-EXPTIME) in the data (resp., combined) complexity. Given that stratified negation is quite limited, it is natural to ask whether the richer and more expressive well-founded negation could be defined for Datalog ±. The well-founded semantics (WFS) for normal (logic) programs [2] is one of the most widely used semantics for nonmonotonic normal programs. Due to its computational properties (differently from the stable model semantics), it is the standard semantics for such programs for database applications. It is thus especially under a data-oriented perspective of great importance for (dealing with very large amounts of data on) the Web (see [3] for a recent survey of Web-related applications of Datalog ±). Having many nice features, the WFS is defined for all normal programs (i.e., logic programs with the possibility of negation in rule bodies), has a polynomial data tractability, approximates the answer set semantics, and coincides with the canonical model in case of stratified normal programs. In [4], we focus on the important problem of defining a WFS for (unrestricted) normal Datalog ± , i.e., Datalog with existentially quantified variables in rule heads and negations in rule bodies. But our research there is guided by the goal of defining a WFS for normal Datalog ± that is close to OWL and its profiles as well as typical DLs, which all have in common that they do not make the unique name assumption (UNA). Thus, the new semantics in [4], called the equality-friendly WFS (EFWFS), also does not make the UNA. The WFS for normal Datalog ± without the UNA, however, actually generalizes neither Datalog ± nor standard normal (logic) programs, which make the UNA, in contrast. The UNA is also rather common in logic programming and databases in general, as well as in some important DLs, such as the DL-Lite family of tractable description logics [5,6]. I.e., the results in this paper (which are technically very different from those in [4]) also allow us to interpret extensions of the DL-Lite-family with nonmonotonic negation using the standard well-founded semantics. The following example demonstrates this for DL-Lite R, ,not from [4].

1994

Given a query to a locally consistent deductive database in a multidatabase federation in which different nodes may cooperate in answering the query, we must take into account the possibility that the cooperating nodes are mutually inconsistent with respect to the queried formula. If we use classical negation, such an inconsistency will manifest itself as the existence of two derivations, one of the queried formula, and one of its negation. We must therefore add a fourth truth value to the three-valued semantics that account for the cases when (i) the queried formula is provable, (ii) its negation is provable, (iii) neither the queried formula, nor its negation are provable.

Journal of Automated Reasoning, 1994

In this paper, we study a new semantics of logic programming and deductive databases. Thepossible model semantics is introduced as a declarative semantics of disjunctive logic programs. The possible model semantics is an alternative theoretical framework to the classical minimal model semantics and provides a flexible inference mechanism for inferring negation in disjunctive logic programs. We also present a proof procedure for the possible model semantics and show that the possible model semantics has an advantage from the computational complexity point of view.

Journal of Logic, Language and Information

Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents’ knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge—or more appropriately, belief—is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we ...

2006

I would like to thank my advisor Prof. Ester Zumpano for her guidance and continuous support during these three years. I would also like to thank Prof. Sergio Greco for his valuable advice and suggestions. I would like to express my gratitude to Prof. Mirosław Truszczyński who has been so deeply involved in our research and who, at the same time, has helped me to explore those aspects of the work which I found particularly interesting. I wish to thank my parents for their patience and affection. Finally, special thanks to all my friends for the various forms of help and encouragement that they have given me. Preliminaries Summary. In this chapter we introduce some basic concepts on logic programming and computational complexity. For a detailed treatment see [10, 11, 86, 105, 106, 117, 125, 142]. We briefly introduce syntax of (disjunctive) logic programs and present the stable model semantics. Moreover, after introducing complexity measures, we survey complexity results of various forms of logic programming. 2 Techniques for Repairing and Querying Summary. This chapter gives an informal description of the main techniques for repairing and querying inconsistent databases proposed in the literature. After a brief introduction to these techniques, some of them will be described in more details.

Web Reasoning and …, 2010

We address the problem of dealing with inconsistencies in Description Logic (DL) knowledge bases. Our general goal is both to study DL semantical frameworks which are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries posed to DL knowledge bases under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We show that, if we use the notion of repair studied in databases, inconsistency-tolerant query answering is intractable, even for the simplest form of queries. Therefore, we study different variants of the repair-based semantics, with the goal of reaching a good compromise between expressive power of the semantics and computational complexity of inconsistency-tolerant query answering.

1997

In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9,16]. It is well-known that there are disjunctive deductive databases where no stable or partial stable models exist, and these databases are called inconsistent w.r.t. the basic semantics. We define a consistent variant of each class of models, which we call evidential stable and partial evidential stable models. It is shown that if a database is already consistent w.r.t. the basic semantics, then the class of evidential models coincides with the basic class of models. Otherwise, the set of evidential models is a subset of the set of minimal models of the database. This subset is non-empty, if the database is logically consistent. It is determined according to a suitable preference relation, whose underlying idea is to minimize the amount of reasoning by contradiction. The technical ingredients for the construction of the new classes of models are two transformations of disjunctive deductive databases. First, the evidential transformation is used to realize the preference relation, and to define evidential stable models. Secondly, based on the tu-transformation the result is lifted to the three-valued case, that is, partial evidential stable models are defined.

Theory and Practice of Logic Programming, 2012

Datalogis one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An importantDatalogextension is DisjunctiveDatalog, which significantly increases the expressivity of the basic language. DisjunctiveDatalogis useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming ofDatalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem,Datalog∃has recently been proposed, which extends traditionalDatalogby existential quantification in rule heads. In this work, we pr...