We study the complexity of conjunctive query answering under (weakly-)(frontier-)guarded disjunctive existential rules, i.e., existential rules extended with disjunction, and their main subclasses, linear rules and inclusion dependencies (IDs). Our main result states that conjunctive query answering under a fixed set of disjunctive IDs is 2EXPTIME-hard. This quite surprising result together with a 2EXPTIME upper bound for weakly-frontier-guarded disjunctive rules, obtained by exploiting recent results on guarded negation first-order logic, gives us a complete picture of the computational complexity of our problem. We also consider a natural subclass of disjunctive IDs, namely frontier-one (only one variable is propagated), for which the combined complexity decreases to EXPTIME. Finally, we show that frontier-guarded rules, combined with negative constraints, are strictly more expressive than DL-Lite H bool , one of the most expressive languages of the DL-Lite family. We also show that query answering under this DL is 2EXPTIME-complete in combined complexity.

The Description Logic EL is used to formulate several large biomedical ontologies. Fuzzy extensions of EL can express the vagueness inherent in many biomedical concepts. We study the reasoning problem of deciding positive subsumption in fuzzy EL with semantics based on general t-norms. We show that the complexity of this problem depends on the specific t-norm chosen. More precisely, if the t-norm has zero divisors, then the problem is co-NP-hard; otherwise, it can be decided in polynomial time. We also show that the best subsumption degree cannot be computed in polynomial time if the t-norm contains the Łukasiewicz t-norm.

A robust system for ontology-based data access should provide meaningful answers to queries even when the data conflicts with the ontology. This can be accomplished by adopting an inconsistency-tolerant semantics, with the consistent query answering (CQA) semantics being the most prominent example. Unfortunately, query answering under the CQA semantics has been shown to be computationally intractable, even when extremely simple ontology languages are considered. In this paper, we address this problem by proposing two new families of inconsistency-tolerant semantics which approximate the CQA semantics from above and from below and converge to it in the limit. We study the data complexity of conjunctive query answering under these new semantics, and show a general tractability result for all known first-order rewritable ontology languages. We also analyze the combined complexity of query answering for ontology languages of the DL-Lite family.

Conjunctive regular path queries are an expressive extension of the well-known class of conjunctive queries and have been extensively studied in the database community. Somewhat surprisingly, there has been little work aimed at using such queries in the context of description logic (DL) knowledge bases, and all existing results target expressive DLs, even though lightweight DLs are considered better-suited for data-intensive applications. This paper aims to bridge this gap by providing algorithms and tight complexity bounds for answering two-way conjunctive regular path queries over DL knowledge bases formulated in lightweight DLs of the DL-Lite and EL families.

One of the most advanced approaches to querying data in the presence of ontologies is to make use of relational database systems, rewriting the original query and the ontology into a new query that is formulated in SQL or, equivalently, in first-order logic (FO). For ontologies written in many standard description logics (DLs), however, such FO-rewritings are not guaranteed to exist. We study FO-rewritings and their existence for a basic class of queries and for ontologies formulated in Horn DLs such as Horn-SHI and EL. Our results include characterizations of the existence of FO-rewritings, tight complexity bounds for deciding whether an FO-rewriting exists (ExpTime and PSpace), and tight bounds on the (worst-case) size of FO-rewritings, when presented as a union of conjunctive queries.

A notion of quantified conditional logics is provided that includes quantification over individual and propositional variables. The former is supported with respect to constant and variable domain semantics. In addition, a sound and complete embedding of this framework in classical higher-order logic is presented. Using prominent examples from the literature it is demonstrated how this embedding enables effective automation of reasoning within (object-level) and about (meta-level) quantified conditional logics with off-the-shelf higher-order theorem provers and model finders.

Among the many approaches for reasoning about degrees of belief inthe presence of noisy sensing and acting, the logical accountproposed by Bacchus, Halpern, and Levesque is perhaps the most expressive.While their formalism is quite general, it is restricted to fluentswhose values are drawn from discrete countable domains, as opposed tothe continuous domains seen in many robotic applications. In thispaper, we show how this limitation in their approach can be lifted.By dealing seamlessly with both discrete distributions and continuousdensities within a rich theory of action, we provide a very generallogical specification of how belief should change after acting andsensing in complex noisy domains.

Artifact-Centric Systems are a novel paradigm in service-oriented computing. In the present contribution we show that model checking bounded, non-uniform artifact-centric systems is undecidable. We provide a partial model checking procedure for artifact-centric systems against the universal fragment of a first-order version of the logic CTL. We obtain this result by introducing a counterpart semantics and developing an abstraction methodology operating on these structures. This enables us to generate finite abstractions of infinite artifact-centric systems, hence perform verification on abstract models.

Recently there has been an increasing interest in incorporating "intensional" functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of "Answer Set Programming Modulo Theories (ASPMT)" — a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that "tight" ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.

Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling. To this end, we design a temporal description logic, TQL, that extends the standard ontology language OWL 2 QL, provides basic means for temporal conceptual modelling and ensures first-order rewritability of conjunctive queries for suitably defined data instances with validity time.