Abstract
PARTHEO, a sound and complete or-parallel theorem prover for first-order logic is presented. The proof calculus is model elimination. PARTHEO consists of a uniform network of sequential theorem provers communicating via message passing. Each sequential prover is implemented as an extension of Warren's abstract machine. PARTHEO is written in parallel C and is running on a network of 16 transputers. The paper comprises a description of the system architecture, the theoretical background, details of the implementation, and results of performance measurements.
This work was supported by the European Community and Nixdorf Computer AG within the ESPRIT project 415F.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Parallel C — User Guide. 3L Ltd., Livingston, Scotland, 1988.
Owen Astrachan. METEOR: Model elimination theorem prover for efficient OR-parallelism. In W.W. Bledsoe, M. Stickel, P. Lincoln, R. Overbeek, and D. Plaisted, editors, 1989 AAAI Spring Symposium on Representation and Compilation in High Performance Theorem Proving: Titles and Abstracts, Stanford, CA, 3 1989.
P.E. Allen, S. Bose, E.M. Clarke, and S. Michaylov. PARTHENON: A Parallel Theorem Prover for Non-Horn Clauses. In CADE 9, pages 764–765, Argonne, Illinois,USA, Springer, 1988.
U. Baron, J. C. de Kergommeaux, M. Hailperin, M. Ratcliffe, M. Robert, J.-Cl. Syre, and H. Westphal. The parallel ECRC Prolog System PEPSys: An Overview and Evaluation Results. In FGCS, ECRC Munich, 1988.
S. Bayerl, W. Ertel, M. v. d. Koelen, F. Kurfess, R. Letz, J. Schumann, Ch. Suttner, and N. Trapp. PARTHEO/6: PARallel Automated THEorem Prover based on the Connection Method for Full First Order Logic — Implementation and Performance. ESPRIT 415F Deliverable D15, 1989.
S. Bayerl, W. Ertel, F. Kurfess, R. Letz, and J. Schumann. D16 / Full First Order Logic PARallel Inference Machine — Language and Design. ESPRIT 415, Deliverables, Brussels, 1989.
E.W. Beth. The Foundations of Mathematics. North-Holland, 1959.
S. Bose, E.M. Clarke, D.E. Long, and S. Michaylov. Parthenon: A Parallel Theorem Prover for Non-Horn Clauses. In LICS, 1989.
W. Bibel. Automated Theorem Proving. Vieweg Verlag, Braunschweig, second edition, 1987.
W.F. Clocksin. Principles of the delPhi Parallel Inference Machine. Comp. Journal, 30(5):386–392, 5 1987.
J. Corbin and M. Bidoit. A Rehabilitation of Robinson's Unification Algorithm. In Information Processing, pages 909–914. North-Holland, 1983.
E. Eder. An Implementation of a Theorem Prover based on the Connection Method. In W. Bibel and B. Petkoff, editors, AIMSA: Artificial Intelligence Methodology Systems Applications, Varna, Bulgaria, 1985. North-Holland.
Ph. Jorrand and Ph. Schnoebelen. Parallel Implementation of Connection Method on an Abstract FP2 Machine. ESPRIT 415F Deliverable D17, 1989.
V. Kumar, Y. Lin, and A. Gupta. Parallel Execution of Logic Programs. In W.W. Bledsoe, M. Stickel, P. Lincoln, R. Overbeek, and D. Plaisted, editors, 1989 AAAI Spring Symposium on Representation and Compilation in High Performance Theorem Proving: Titles and Abstracts, Stanford, CA, 3 1989.
R. Letz and J. Schumann. Global Variables in Logic Programming. Technical report, ATP-Report, Technische Universität München, 1988.
R. Letz, S. Bayerl, J. Schumann, and W. Bibel. SETHEO — A High-Performance Theorem Prover. (to appear in Journal of Automated Reasoning), 1990.
D.W. Loveland. Automated Theorem Proving: a Logical Basis. North-Holland, 1978.
J. Pelletier and P. Rudnicki. Non-obviousness. AAR Newsletter 6, pages 4–5, 1986.
Frank Pfenning. Single Axioms in the Implicational Propositional Calculus. In CADE 9, pages 710–713, Argonne, Illinois, USA, Springer, 1988.
D. A. Plaisted. The Occur-check Problem in Prolog. New Generation Computing, 2:309–322, 1984.
J. Schumann, N. Trapp, and M. van der Koelen. SETHEO: User's Manual. Technical report, ATP-Report, Technische Universität München, 1989.
R.M. Smullyan. First Order Logic. Springer, 1968.
M.A. Stickel. A Prolog Technology Theorem Prover: Implementation by an Extended Prolog Compiler. Journal of Automated Reasoning, 4:353–380, 1988.
J. Vlahavas and C. Halatsis. A New Abstract Prolog Instruction Set. In 7th International Workshop of Expert Systems and Applications, pages 1025–1050, Avignon, 1987.
D.H.D Warren. An Abstract PROLOG Instruction Set. Technical report, SRI, Menlo Park, CA, USA, 1983.
D.H.D. Warren. Parallel Execution Models and Architectures for Prolog. Presented at Working Group Architecture, ESPRIT 415, 1 1988.
G.A. Wilson and J. Minker. Resolution, Refinements, and Search Strategies: a Comparative Study. IEEE Transactions on Computers, C-25:782–801, 8 1976.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schumann, J., Letz, R. (1990). Partheo: A high-performance parallel theorem prover. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_78
Download citation
DOI: https://doi.org/10.1007/3-540-52885-7_78
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52885-2
Online ISBN: 978-3-540-47171-4
eBook Packages: Springer Book Archive