Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations

Ensuring Query Compatibility with Evolving XML Schemas

During the life cycle of an XML application, both schemas and queries may change from one version to another. Schema evolutions may affect query results and potentially the validity of produced data. Nowadays, a challenge is to assess and accommodate the impact of theses changes in rapidly evolving XML applications. This article proposes a logical framework and tool for verifying forward/backward compatibility issues involving schemas and queries. First, it allows analyzing relations between schemas. Second, it allows XML designers to identify queries that must be reformulated in order to produce the expected results across successive schema versions. Third, it allows examining more precisely the impact of schema changes over queries, therefore facilitating their reformulation

Conservative Extensions and Satisfiability in Fragments of First-Order Logic : Complexity and Expressive Power

In this thesis, we investigate the decidability and computational complexity of (deductive) conservative extensions in expressive fragments of first-order logic, such as two-variable and guarded fragments. Moreover, we also investigate the complexity of (query) conservative extensions in Horn description logics with inverse roles. Aditionally, we investigate the computational complexity of the satisfiability problem in the unary negation fragment of first-order logic extended with regular path expressions. Besides complexity results, we also study the expressive power of relation-changing modal logics. In particular, we provide translations intto hybrid logic and compare their expressive power using appropriate notions of bisimulations

Heuristic Ranking in Tightly Coupled Probabilistic Description Logics

The Semantic Web effort has steadily been gaining traction in the recent years. In particular,Web search companies are recently realizing that their products need to evolve towards having richer semantic search capabilities. Description logics (DLs) have been adopted as the formal underpinnings for Semantic Web languages used in describing ontologies. Reasoning under uncertainty has recently taken a leading role in this arena, given the nature of data found on theWeb. In this paper, we present a probabilistic extension of the DL EL++ (which underlies the OWL2 EL profile) using Markov logic networks (MLNs) as probabilistic semantics. This extension is tightly coupled, meaning that probabilistic annotations in formulas can refer to objects in the ontology. We show that, even though the tightly coupled nature of our language means that many basic operations are data-intractable, we can leverage a sublanguage of MLNs that allows to rank the atomic consequences of an ontology relative to their probability values (called ranking queries) even when these values are not fully computed. We present an anytime algorithm to answer ranking queries, and provide an upper bound on the error that it incurs, as well as a criterion to decide when results are guaranteed to be correct.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

Deciding Second-order Logics using Database Evaluation Techniques

We outline a novel technique that maps the satisfiability problems of second-order logics, in particular WSnS (weak monadic second-order logic with n successors), S1S (monadic second-order logic with one successor), and of μ-calculus, to the problem of query evaluation of Complex-value Datalog queries. In this dissertation, we propose techniques that use database evaluation and optimization techniques for automata-based decision procedures for the above logics. We show how the use of advanced implementation techniques for Deductive databases and for Logic Programs, in particular the use of tabling, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique, in particular we consider variants of tabling and goal reordering. We then show that the decision problem for S1S can be mapped to the problem of query evaluation of Complex-value Datalog queries. We explore optimizations that can be applied to various types of formulas. Last, we propose analogous techniques that allow us to approach μ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we outline a top-down evaluation technique to drive our incremental procedure and propose heuristics that guide the problem partitioning to reduce the size of the problems that need to be solved

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200