We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the Inside-Outside algorithm. 1.

The well-founded semantics has gained wide acceptance partly because it is a skeptical semantics. That is, the well-founded model posits as unknown atoms which are deemed true or false in other formalisms such as stable models. This skepticism makes the well-founded model not only useful in itself, but also suitable as a basis for other forms of non-monotonic reasoning. For instance, since algorithms to compute stable models are intractable, the atoms relevant tosuch algorithms can be limited to those unde ned in the well-founded model. This paper presents an implementation ofthewell-founded semantics in the SLG-WAM of XSB. To compute the well-founded semantics, the SLG-WAM adds three operations to its tabling engine | negative loop detection, delay and simplication | which serve to detect, to break and to resolve cycles through negation that may arise in evaluating normal programs. We describe fully the addition of these operations to our tabling engine, and demonstrate the e ciency of our implementation in two ways. First, we present a theorem that bounds the need for delay to those literals which are not dynamically strati ed for a xed-order computation. Secondly, we present performance results that indicate that the overhead of delay and simpli cation to Prolog | or tabled | evaluations is minimal. 1

Elf is a general meta-language for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. The traditional logic programming paradigm is extended by replacing first-order terms with dependently typed -terms and allowing implication and universal quantification in the bodies of clauses. These higher-order features allow us to model concisely and elegantly conditions on variables and the discharge of assumptions which are prevalent in many logical systems. However, many specifications are not executable under the traditional logic programming semantics and performance may be hampered by redundant computation. To address these problems, I propose a tabled higher-order logic programming interpretation for Elf. Some redundant computation is eliminated by memoizing sub-computation and re-using its result later. If we do not distinguish different proofs for a property, then search based on tabled logic programming is complete and terminates for programs with bounded recursion. In this proposal, I present a proof-theoretical characterization for tabled higher-order logic programming. It is the basis of the implemented prototype for tabled logic programming interpreter for Elf. Preliminary experiments indicate that many more logical specifications are executable under the tabled semantics. In addition, tabled computation leads to more efficient execution of programs. The goal of the thesis is to demonstrate that tabled logic programming allows us to efficiently automate reasoning with and about logical systems in the logical f...

We provide a first investigation of the specialisation and transformation of tabled logic programs through unfolding. We show that --- surprisingly --- unfolding, even determinate, can worsen the termination behaviour in the context of tabling. We therefore establish two criteria which ensure that such mishaps are avoided. We also briefly discuss the influence of some other transformation techniques on the termination and efficiency of tabled logic programs.

The semantic web is a promising application-area for the Prolog programming language for its non-determinism and pattern-matching. In this paper we outline an infrastructure for loading and saving RDF/XML, storing triples, elementary reasoning with triples and visualization. A predecessor of the infrastructure described here has been used in various applications for ontology-based annotation of multimedia objects using semantic web languages. Our library aims at fast parsing, fast access and scalability for fairly large but not unbounded applications upto 40 million triples.

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Actual performance of Prolog based applications largely depends on how the underlying system implements memory management.

This article describes a simple and ecient way of using a logic programming language with built-in tabulation for general purpose semantics-based program analysis. The simplicity of the method is based on a clear separation of abstraction and control: conceptually, a concrete program is executed over an abstract domain and the tabulation mechanism avoids recomputation, ensures termination and collects the results of the analysis. The efficiency derives from the fact that an abstract interpreter induces an abstract compiler which maps input programs to corresponding abstract programs which are (compiled and) run in XSB [43]. The design of new analyses is an easy and fast process, because XSB is a general purpose logic programming system which supports efficient fix-point computations through tabling implemented at the abstract machine level and comes off the shelf: in fact, due to its optimized control and superior tabling performance, our approach using XSB competitively compares with most of the existing special purpose abstract interpretation tools for logic programs. We demonstrate that our approach to using XSB for abstract interpretation supports the usual techniques and optimizations of other frameworks in a straightforward and flexible way.

Given are a directed edge-labelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this problem using relational algebra, and show how it may be implemented in Prolog. The motivation for the problem derives from a declarative framework for specifying compiler optimisations. 1 Bob Paige and IFIP WG 2.1 Bob Paige was a long-standing member of IFIP Working Group 2.1 on Algorithmic Languages and Calculi. In recent years, the main aim of this group has been to investigate the derivation of algorithms from specifications by program transformation. Already in the mid-eighties, Bob was way ahead of the pack: instead of applying transformational techniques to well-worn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [16, 48, 52]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular

The use of tabling in logic programming has been recognized as a powerful evaluation technique. Currently available tabling systems are mostly based on variant checks and hence are limited in their ability to recognize reusable subcomputations. Tabling systems based on call subsumption can yield superior performance by recognizing a larger set of reusable computations. However, a straightforward adaptation of the mechanisms used in variant-based systems to reuse these computations can in fact result in considerable performance degradation. In this paper we propose a novel organization of tables using Dynamic Threaded Sequential Automata (DTSA) which permits efficient reuse of previously computed results in a subsumptive system. We describe an implementation of the tables using DTSA and the associated access mechanisms. We also report experimental results which show that a subsumptive tabling system implemented by extending the XSB logic programmingsystem with our table access techniqu...