Logic Programming as Constructivism

The features of logic programming that seem unconventional from the viewpoint of classical logic can be explained in terms of constructivistic logic. We motivate and propose a constructivistic proof theory of non-Horn logic programming. Then, we apply this formalization for establishing results of practical interest. First, we show that 'stratification can be motivated in a simple and intuitive way. Relying on similar motivations, we introduce the larger classes of 'loosely stratified' and 'constructively consistent' programs. Second, we give a formal basis for introducing quantifiers into queries and logic programs by defining 'constructively domain independent* formulas. Third, we extend the Generalized Magic Sets procedure to loosely stratified and constructively consistent programs, by relying on a 'conditional fixpoini procedure

Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries

Conjunctive database queries have been extended with a mechanism for object creation to capture important applications such as data exchange, data integration, and ontology-based data access. Object creation generates new object identifiers in the result, that do not belong to the set of constants in the source database. The new object identifiers can be also seen as Skolem terms. Hence, object-creating conjunctive queries can also be regarded as restricted second-order tuple-generating dependencies (SO tgds), considered in the data exchange literature. In this paper, we focus on the class of single-function object-creating conjunctive queries, or sifo CQs for short. We give a new characterization for oid-equivalence of sifo CQs that is simpler than the one given by Hull and Yoshikawa and places the problem in the complexity class NP. Our characterization is based on Cohen's equivalence notions for conjunctive queries with multiplicities. We also solve the logical entailment problem for sifo CQs, showing that also this problem belongs to NP. Results by Pichler et al. have shown that logical equivalence for more general classes of SO tgds is either undecidable or decidable with as yet unknown complexity upper bounds.Comment: This revised version has been accepted on 11 January 2016 for publication in The VLDB Journa

Maintaining Distributed Recursive Views Incrementally

This paper proposes an algorithm to compute incrementally the changes to distributed recursive database views in response to insertions and deletions of base facts. Our algorithm uses a pipelined semi-näıve (PSN) evaluation strategy introduced in declarative networking. Unlike prior work, our algorithm is formally proven to be correct for recursive query computation in the presence of message reordering in the system. Our proof proceeds in two stages. First, we show that all the operations performed by our PSN algorithm computes the same set of results as traditional centralized semi-näıve evaluation. Second, we prove that our algorithm terminates, even in the presence of cyclic derivations due to recursion

Converging to the Chase - a Tool for Finite Controllability

We solve a problem, stated in [CGP10], showing that Sticky Datalog, defined in the cited paper as an element of the Datalog\pm project, has the finite controllability property. In order to do that, we develop a technique, which we believe can have further applications, of approximating Chase(D, T), for a database instance D and some sets of tuple generating dependencies T, by an infinite sequence of finite structures, all of them being models of T

Bottom-up evaluation of HiLog in the context of deductive database systems

Bibliography: leaves 127-130.HiLog is a logic-based language which boasts the expressiveness of a higher-order syntax while retaining the simplicity of a first-order semantics. This work examines the suitability of Horn-clause HiLog as a query language for deductive databases by investigating the feasibility of adapting well-established Datalog evaluation algorithms for the evaluation of HiLog programs. Each of the evaluation algorithms examined in the work is formally described and verified in terms of completeness and correctness. Furthermore, a practical HiLog evaluator based on each algorithm verifies the feasibility of its implementation in a real-world context. It is demonstrated that the Datalog evaluation algorithms do indeed have realistic HiLog analogs. The work also compares the performance of these analogs