Abstract
The inverse method is a generalization of resolution that can be applied to non-classical logics. We have recently shown how Andreoli’s focusing strategy can be adapted for the inverse method in linear logic. In this paper we introduce the notion of focusing bias for atoms and show that it gives rise to forward and backward chaining, generalizing both hyperresolution (forward) and SLD resolution (backward) on the Horn fragment. A key feature of our characterization is the structural, rather than purely operational, explanation for forward and backward chaining. A search procedure like the inverse method is thus able to perform both operations as appropriate, even simultaneously. We also present experimental results and an evaluation of the practical benefits of biased atoms for a number of examples from different problem domains.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andreoli, J.-M.: Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2(3), 297–347 (1992)
Andreoli, J.-M.: Focussing and proof construction. Annals of Pure and Applied Logic 107, 131–163 (2001)
Cervesato, I., Pfenning, F., Walker, D., Watkins, K.: A concurrent logical framework I & II. Technical Report CMU-CS-02-101 and 102, Department of Computer Science, Carnegie Mellon University, 2002. Revised (May 2003)
Chaudhuri, K., Pfenning, F.: A focusing inverse method theorem prover for first-order linear logic. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 69–83. Springer, Heidelberg (2005)
Chaudhuri, K., Pfenning, F.: Focusing the inverse method for linear logic. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 200–215. Springer, Heidelberg (2005)
Degtyarev, A., Voronkov, A.: The inverse method. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 179–272. MIT Press, Cambridge (2001)
Gentzen, G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 176–210 (1935): Szabo, M.E.: The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1969)
Girard, J.-Y.: Locus solum: from the rules of logic to the logic of rules. Mathematical Structures in Computer Science 11, 301–506 (2001)
Hodas, J.S., Miller, D.: Logic programming in a fragment of intuitionistic linear logic. Information and Computation 110(2), 327–365 (1994)
Jacob, M.: Howe. Proof Search Issues in Some Non-Classical Logics. PhD thesis, University of St. Andrews (September 1998)
Kowalski, R., Kuehner, D.: Linear resolution with selection function. Artificial Intelligence 2, 227–260 (1971)
Lincoln, P., Mitchell, J.C., Scedrov, A., Shankar, N.: Decision problems for propositional linear logic. Annals of Pure and Applied Logic 56, 239–311 (1992)
Mantel, H., Otten, J.: LinTAP: A tableau prover for linear logic. In: Murray, N.V. (ed.) TABLEAUX 1999. LNCS (LNAI), vol. 1617, pp. 217–231. Springer, Heidelberg (1999)
Miller, D.: A multiple-conclusion meta-logic. In: Abramsky, S. (ed.) Ninth Annual Symposium on Logic in Computer Science, Paris, France, July 1994, pp. 272–281. IEEE Computer Society Press, Los Alamitos (1994)
Sahlin, D., Franzén, T., Haridi, S.: An intuitionistic predicate logic theorem prover. Journal of Logic and Computation 2(5), 619–656 (1992)
Tammet, T.: Resolution, inverse method and the sequent calculus. In: Gottlob, G., Leitsch, A., Mundici, D. (eds.) KGC 1997. LNCS, vol. 1289, pp. 65–83. Springer, Heidelberg (1997)
Tamura, N.: Llprover. At: http://bach.istc.kobe-u.ac.jp/llprover
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chaudhuri, K., Pfenning, F., Price, G. (2006). A Logical Characterization of Forward and Backward Chaining in the Inverse Method. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_9
Download citation
DOI: https://doi.org/10.1007/11814771_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37187-8
Online ISBN: 978-3-540-37188-5
eBook Packages: Computer ScienceComputer Science (R0)