# Proof-theoretic characterisations of logic programming

Communications

First Online:

## Abstract

A characterisation of a logic programming system is given in the form of a natural deduction proof system. The proof system is proven to be “equivalent” to an operational semantics for the logic programming system, in the sense that the set of theorems of the proof system is exactly the set of existential closures of queries solvable in the operational semantics. It is argued that this proof-theoretic characterisation captures our intuitions about logic programming better than do traditional characterisations, such as those using resolution or fixpoint semantics.

## Preview

Unable to display preview. Download preview PDF.

## References

- [And89]James H. Andrews. Proof-theoretic characterisations of logic programming. Technical Report LFCS-89-77, Laboratory for the Foundations of Computer Science, University of Edinburgh, Edinburgh, Scotland, May 1989.Google Scholar
- [Cla78]K. L. Clark. Negation as failure. In
*Logic and Data Bases*, pages 293–322, New York, 1978. Plenum Press.Google Scholar - [Cla79]K. L. Clark. Predicate logic as a computational formalism. Technical Report 79/59 TOC, Department of Computing, Imperial College, London, December 1979.Google Scholar
- [Gen69]Gerhardt Gentzen.
*The Collected Papers of Gerhard Gentzen*. North-Holland, Amsterdam, 1969. Ed. M. E. Szabo.Google Scholar - [Llo84]John W. Lloyd.
*Foundations of Logic Programming*. Springer-Verlag, Berlin, 1984.Google Scholar - [ML71]Per Martin-Löf. Hauptsatz for the intuitionistic theory of iterated inductive definitions. In J. E. Fenstad, editor,
*Proceedings of the Second Scandinavian Logic Symposium*. North-Holland, 1971.Google Scholar - [Plo81]Gordon Plotkin. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, September 1981.Google Scholar
- [Smu68]Raymond M. Smullyan.
*First-Order Logic*. Springer-Verlag, Berlin, 1968.Google Scholar - [Sun83]Göran Sundholm. Systems of deduction. In D. Gabbay and F. Guenther, editors,
*Handbook of Philosophical Logic*, pages 133–188. D. Reidel, Dordrecht, 1983.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1989