An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...

The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, well-founded orderings serve as a starting point for tackling this so-called "global termination" problem. Polyvariance is determined by the set of distinct "partially deduced" atoms generated during partial deduction. Avoiding ad-hoc techniques, we formulate a quite general framework where this set is represented as a tree structure. Associating weights with nodes, we define a well-founded order among such structures, thus obtaining a foundation for certified global termination of partial deduction. We include an algorithm template, concrete instances of which can be used in actual implementations, prove termination and correctness, and report on the results of some experiments. Finally, we conjecture that the proposed framewor...

. Recently, partial deduction of logic programs has been extended to conceptually embed folding. To this end, partial deductions are no longer computed of single atoms, but rather of entire conjunctions; Hence the term "conjunctive partial deduction". Conjunctive partial deduction aims at achieving unfold/fold-like program transformations such as tupling and deforestation within fully automated partial deduction. However, its merits greatly surpass that limited context: Also other major efficiency improvements are obtained through considerably improved side-ways information propagation. In this extended abstract, we investigate conjunctive partial deduction in practice. We describe the concrete options used in the implementation(s), look at abstraction in a practical Prolog context, include and discuss an extensive set of benchmark results. From these, we can conclude that conjunctive partial deduction indeed pays off in practice, thoroughly beating its conventional precursor on a wide...

Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higher-order HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.

Automated theorem proving has made great progress during the last few decades. Proofs of more and more difficult theorems are being found faster and faster. However, the exponential increase in the size of the search space remains for many theorem proving problems. Logic program analysis and transformation techniques have also made progress during the last few years and automated theorem proving can benefit from these techniques if they can be made applicable to general theorem proving problems. In this thesis we investigate the applicability of logic program analysis and transformation techniques to automated theorem proving. Our aim is to speed up theorem provers by avoiding useless search. This is done by detecting and deleting parts of the theorem prover and theory under consideration that are not needed for proving a given formula. The analysis and transformation techniques developed for logic programs can be applied in automated theorem proving via a programming technique called ...

Analysis and transformation techniques developed for logic programming can be successfully applied to automatic theorem proving. In this paper we demonstrate how these techniques can be used to infer useful information that can speed up theorem provers, assist in the identi cation of necessary inference rules for solving speci c problems, how failure branches can be eliminated from the proof tree and how a non-terminating deduction in a proof system can be turned into failure. In addition, this method also provides su cient conditions for identifying Case-free Theories [26]. The specialisation techniques developed in this paper are independent of the proof system and can therefore be applied to theorem provers for any logic written as logic programs. 2 1

In this paper we describe a method of program specialisation and give an extended example of its application to specialisation of a refutation proof procedure for rst order logic. In the specialisation method, a partial evaluation of the proof procedure with respect to a given theory is rst obtained. Secondly an abstract interpretation of the partially evaluated program is computed, and this is used to detect and remove clauses that yield no solutions (useless clauses). A proof is given that such clauses can be deleted from a normal program while preserving the results of all nite computations. The model elimination proof procedure described in [20] is specialised with respect to given theories, and the negative ancestor check inference rule can be eliminated in cases where it is not relevant. Our results for the model elimination prover, obtained by general-purpose transformations, are comparable to those obtained in [20] by a special-purpose analysis. It is shown that specialisations of the proof procedure can be achieved that cannot be obtained by partial evaluation. The method is applicable to any normal program, and thus provides an extension of the power of partial evaluation.

This paper presents an introduction for the ESPRIT community of the recently started ESPRIT 11 project, PLUS (P5254). The goal of the project is the production of a robust natural language dialogue system integrating linguistic and non-linguistic knowledge in a principled way, based on the pragmatics theories of Grice and Searle, and using results in knowledge-base management systems and logic programming for the maintenance of dynamic contextual knowledge bases. We present the background assumptions, an overview of the system conceptual design, of the empirical research that has already been undertaken on real corpora and of re-usable system components. 1