Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.

We identify three classes of four-state paraconsistent logics according to their different approaches towards the disjunctive syllogism, and investigate three representatives of these approaches: Quasi-classical logic, which always accepts this principle, Belnap's logic, that rejects the disjunctive syllogism altogether, and a logic of inconsistency minimization that restricts its application to consistent fragments only. These logics are defined in a syntactic and a semantic style, which are linked by a simple transformation. It is shown that the three formalisms accommodate knowledge minimization, and that the most liberal formalism towards the disjunctive syllogism is also the strongest among the three, while the most cautious logic is the weakest one.

The DL-Lite family of Description Logics has been designed with the specific goal of allowing for answering complex queries (in particular, conjunctive queries) over ontologies with very large instance sets (ABoxes). So far, in DL-Lite systems, this goal has been actually achieved only for relatively simple (short) conjunctive queries. In this paper we present Presto, a new query answering technique for DL-Lite ontologies, and an experimental comparison of Presto with the main previous approaches to query answering in DL-Lite. In practice, our experiments show that, in real ontologies, current techniques are only able to answer conjunctive queries of less than 7-10 atoms (depending on the complexity of the TBox), while Presto is actually able to handle conjunctive queries of up to 30 atoms. Furthermore, in the cases that are already successfully handled by previous approaches, Presto is significantly more efficient.

We investigate the computational complexity of axiom pinpointing, which is the task of finding minimal subsets of a Description Logic knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.

Horn fragments of Description Logics (DLs) have gained popularity because they provide a beneficial trade-off between expressive power and computational complexity and, more specifically, are usually tractable w.r.t. data complexity. Despite their potential, and partly due to the intricate interaction of nominals (O), inverses (I) and counting (Q), such fragments had not been studied so far for the DLs SHOIQ and SROIQ that underly OWL 1 and 2. In this paper, we present a polynomial and modular translation from Horn-SHOIQ knowledge bases into DATALOG, which shows that standard reasoning tasks are feasible in deterministic single exponential time. This improves over the previously known upper bounds, and contrasts the known NEXPTIME completeness of full SHOIQ. Thereby, Horn-SHOIQ stands out as the first EXPTIME complete DL that allows simultaneously for O, I, and Q. In addition, we show that standard reasoning in Horn-SROIQ is 2-EXPTIME complete. Despite their high expressiveness, both Horn-SHOIQ and Horn-SROIQ have polynomial data complexity. This makes them particularly attractive for reasoning in semantically enriched systems with large data sets. A promising first step in this direction could be achieved exploiting existing DATALOG engines, along the lines of our translation.

Databases and related information systems can benefit from the use of ontologies to enrich the data with general background knowledge. The DL-Lite family of ontology languages was specifically tailored towards such ontology-based data access, enabling an implementation in a relational database management system (RDBMS) based on a query rewriting approach. In this paper, we propose an alternative approach to implementing ontology-based data access in DL-Lite. The distinguishing feature of our approach is to allow rewriting of both the query and the data. We show that, in contrast to the existing approaches, no exponential blowup is produced by the rewritings. Based on experiments with a number of real-world ontologies, we demonstrate that query execution in the proposed approach is often more efficient than in existing approaches, especially for large ontologies. We also show how to seamlessly integrate the data rewriting step of our approach into an RDBMS using views (which solves the update problem) and make an interesting observation regarding the succinctness of queries in the original query rewriting approach.

Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontologies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into independent parts. In this paper, we study decompositions that are syntax independent in the sense that the resulting partitioning depends only on the meaning of the vocabulary items, but not on the concrete syntactic form of the axioms in the ontology. We present the first systematic investigation of decompositions of this type in the context of ontologies. Specifically, we focus on ontologies formulated in description logics and provide a variety of results that range from theorems stating the existence of unique finest decompositions to complexity results and algorithms computing decompositions. We also investigate the relationship between the existence of unique finite decompositions and a variant of the Craig interpolation property called parallel interpolation.

Description Logics (DLs) are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries (CQs), the standard query language in databases, have recently gained significant attention for querying DL knowledge bases. Several different techniques are available for a wide range of DLs. Nevertheless, for OWL 1 DL and OWL 2 DL, decidability of CQ entailment is an open problem. So far, the combination of nominals, inverse roles, and number restrictions caused unsolvable problems. We tackle this problem and present a decidability result for entailment of unions of CQs in a DL with all three problematic constructors. For queries with only simple roles, our result also shows decidability in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards CQ entailment decision procedures for OWL.

There is currently a growing interest in techniques for hiding parts of the signature of an ontology Kh that is being reused by another ontology Kv. Towards this goal, Cuenca Grau, Motik, and Kazakov (2009) recently proposed the import-by-query framework, which makes the content of Kh accessible through a limited query interface. If Kv reuses the symbols from Kh in a certain restricted way, one can reason over Kv U Kh by accessing only Kv and the query interface. In this paper, we map out the landscape of the import-by-query problem. We show that certain restrictions of our original framework are strictly necessary to make reasoning possible, we propose extensions that overcome some of the expressivity limitations, we present several novel reasoning algorithms, and we outline the limitations of the new framework.

This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i.e., the validity of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic is decidable) nor for the positive satisfiability problem, because quasi-witnessed interpretations are particularly adequate for the infinite-valued Product Logic. We give an algorithm that reduces the problem of validity (and satisfiability) of assertions in our Fuzzy Description Logic (restricted to quasi-witnessed interpretations) to a semantic consequence problem, with finite number of hypothesis, on infinite-valued propositional Product Logic.