A Framework for Program Development Based on Schematic Proof

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach

Parallel execution of horn claus programs

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Incorporating Stratified Negation into Query-Subquery Nets for Evaluating Queries to Stratified Deductive Databases

Most of the previously known evaluation methods for deductive databases are either breadth-first or depth-first (and recursive). There are cases when these strategies are not the best ones. It is desirable to have an evaluation framework for stratified DatalogN that is goal-driven, set-at-a-time (as opposed to tuple-at-a-time) and adjustable w.r.t. flow-of-control strategies. These properties are important for efficient query evaluation on large and complex deductive databases. In this paper, by incorporating stratified negation into so-called query-subquery nets, we develop an evaluation framework, called QSQNSTR, with such properties for evaluating queries to stratified DatalogN databases. A variety of flow-of-control strategies can be used for QSQNSTR. The generic evaluation method QSQNSTR for stratified DatalogN is sound, complete and has a PTIME data complexity

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Proceedings of the Workshop on the lambda-Prolog Programming Language

The expressiveness of logic programs can be greatly increased over first-order Horn clauses through a stronger emphasis on logical connectives and by admitting various forms of higher-order quantification. The logic of hereditary Harrop formulas and the notion of uniform proof have been developed to provide a foundation for more expressive logic programming languages. The λ-Prolog language is actively being developed on top of these foundational considerations. The rich logical foundations of λ-Prolog provides it with declarative approaches to modular programming, hypothetical reasoning, higher-order programming, polymorphic typing, and meta-programming. These aspects of λ-Prolog have made it valuable as a higher-level language for the specification and implementation of programs in numerous areas, including natural language, automated reasoning, program transformation, and databases

Fault detection and rectification algorithms in a question-answering system

A Malay proverb "jika sesat di hujung jalan, baleklah kepangkal jalan" roughly means "if you get lost at the end of the road, go back to the beginning". In going back to the beginning of the road, we learn our mistakes and hopefully will not repeat the same mistake again. Thus, this work investigates the use of formal logic as a practical tool for reasoning why we could not infer or deduce a correct answer from a question posed to a database. An extension of the Prolog interpreter is written to mechanise a theorem-proving system based on Horn clauses. This extension procedure will form the basis of the question-answering system. Both input into and output from this system is in the form of predicate calculus. This system can answer all four classes of questions as classified by Chang and Lee (1973). [Continues.

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions