Transformation-Based Bottom-Up Computation of the Well-Founded Model

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass and Dix for disjunctive programs. However, even if we restrict their framework to nondisjunctive programs, their residual program can grow to exponential size, whereas for function-free programs our program remainder is always polynomial in the size of the extensional database (EDB). We show that particular orderings of our transformations (we call them strategies) correspond to well-known computational methods like the alternating fixpoint approach, the well-founded magic sets method and the magic alternating fixpoint procedure. However, due to the confluence of our calculi, we come up with computations of the well-founded model that are provably better than these methods. In contrast to other approaches, our transformation method treats magic set transformed programs correctly, i.e. it always computes a relevant part of the well-founded model of the original program.Comment: 43 pages, 3 figure

Magic Sets for Disjunctive Datalog Programs

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimization technique. An important feature of disjunctive Datalog is nonmonotonicity, which calls for nondeterministic implementations, such as backtracking search. A distinguishing characteristic of the new method is that the optimization can be exploited also during the nondeterministic phase. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query under these assumptions. This allows for dynamic pruning of the search space. In contrast, the effect of the previously defined MS methods for disjunctive Datalog is limited to the deterministic portion of the process. In this way, the potential performance gain by using the proposed method can be exponential, as could be observed empirically. The correctness of MS is established thanks to a strong relationship between MS and unfounded sets that has not been studied in the literature before. This knowledge allows for extending the method also to programs with stratified negation in a natural way. The proposed method has been implemented in DLV and various experiments have been conducted. Experimental results on synthetic data confirm the utility of MS for disjunctive Datalog, and they highlight the computational gain that may be obtained by the new method w.r.t. the previously proposed MS methods for disjunctive Datalog programs. Further experiments on real-world data show the benefits of MS within an application scenario that has received considerable attention in recent years, the problem of answering user queries over possibly inconsistent databases originating from integration of autonomous sources of information.Comment: 67 pages, 19 figures, preprint submitted to Artificial Intelligenc

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP

Moa and the multi-model architecture: a new perspective on XNF2

Advanced non-traditional application domains such as geographic information systems and digital library systems demand advanced data management support. In an effort to cope with this demand, we present the concept of a novel multi-model DBMS architecture which provides evaluation of queries on complexly structured data without sacrificing efficiency. A vital role in this architecture is played by the Moa language featuring a nested relational data model based on XNF2, in which we placed renewed interest. Furthermore, extensibility in Moa avoids optimization obstacles due to black-box treatment of ADTs. The combination of a mapping of queries on complexly structured data to an efficient physical algebra expression via a nested relational algebra, extensibility open to optimization, and the consequently better integration of domain-specific algorithms, makes that the Moa system can efficiently and effectively handle complex queries from non-traditional application domains

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200