Abstract
In this paper we propose a non-clausal representational formalism (of definite formulas) that retains the syntactic flavor and algorithmic advantages of Horn clauses. The notion of a definite formula is generic in the sense that it is available to any logical calculus. We argue that efficient automated reasoning techniques which utilize definite formula representation of knowledge (such as SLD-resolution) can be developed for classical and a variety of non-classical logics.
Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
Preview
Unable to display preview. Download preview PDF.
References
HÄhnle, R., Murray, N. and Rosenthal, E.: Completeness for Linear Regular Negation Normal Form Inference Systems. State University of New York, Albany, Technical Report 97-2 (1997).
Lloyd, J. W.: Foundations of Logic Programming, 2nd ed. Springer-Verlag (1987).
Malinowski, G.: Many-Valued Logics. Oxford University Press (1993).
Manna, Z. and Waldinger, R.: Special Relations in Automated Deduction. J. ACM 33 (1986) 1–59.
McAllester, D.: Truth Maintenance. Proc. AAAI-90 (1990) 1109–1116.
Murray, N.: Completely Non-Clausal Theorem Proving. Artificial Intelligence 18 (1982) 67–85.
Robinson, J.A.: A Machine-Oriented Logic Based on the Resolution Principle. J. ACM 12 (1965) 23–41.
Roy-Chowdhury, R. and Dalai, M.: Model Theoretic Semantics and Tractable Algorithm for CNF-BCP. Proc. AAAI-97 (1997) 227–232.
Shankar, S. and Slage, J.: Connection Based Strategies for Deciding Prepositional Temporal Logic. Proc. AAAI-97 (1997) 172–177.
Stachniak, Z.: Resolution Proof Systems: An Algebraic Theory. Kluwer Academic Publishers (1996).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stachniak, Z. (1998). Non-clausal reasoning with propositional definite theories. In: Calmet, J., Plaza, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 1998. Lecture Notes in Computer Science, vol 1476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055921
Download citation
DOI: https://doi.org/10.1007/BFb0055921
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64960-1
Online ISBN: 978-3-540-49816-2
eBook Packages: Springer Book Archive