Abstract
In this paper we study the completeness of resolution when it is restricted by a non-liftable order and by weak subsumption. A non-liftable order is an order that does not satisfy A≺B⇒AΘ≺BΘ. Clause c 1 weakly subsumes c 2 if c 1Θ C⊂c 2, and Θ is a renaming substitution. We show that it is natural to distinguish 2 types of non-liftable orders and 3 types of weak subsumption, which correspond naturally to the 2 types of non-liftable orders. Unfortunately all natural combinations are not complete. The problem of the completeness of resolution with non-liftable orders was left open in ([Nivelle96]). We will also give some good news: Every non-liftable order is complete for clauses of length 2, and can be combined with weak subsumption.
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References
R.S. Boyer, Locking: A Restriction of Resolution, Ph. D. Thesis, University of Texas at Austin, Texas 1971.
C.-L. Chang, R. C-T. Lee, Symbolic logic and mechanical theorem proving, Academic Press, New York 1973.
C. Fermüller, A. Leitsch, T. Tammet, N. Zamov, Resolution Methods for the Decision Problem, Springer Verlag, 1993.
W.H. Joyner, Resolution Strategies as Decision Procedures, J. ACM 23, 1 (July 1976), pp. 398–417.
A. Leitsch, On Some Formal Problems in Resolution Theorem Proving, Yearbook of the Kurt Gödel Society, pp. 35–52, 1988.
D. W. Loveland, Automated Theorem Proving, a Logical Basis, North Holland Publishing Company, Amsterdam, New York, Oxford, 1978.
Resolution Games and Non-Liftable Resolution Orderings, in CSL 94, pp. 279–293, Springer Verlag, Kazimierz, Poland, 1994.
H. de Nivelle, Ordering Refinements of Resolution, Ph. D. thesis, Delft University of Technology, 1995.
Resolution Games and Non-Liftable Resolution Orderings, the Annals of the Kurt Gödel Society, 1996.
J. Reynolds, Unpublished Seminar Notes, Stanford University, Palo Alto, California, 1966.
J.A. Robinson, A Machine Oriented Logic Based on the Resolution Principle, Journal of the ACM, Vol. 12, pp 23–41, 1965.
T. Tammet, Seperate Orderings for Ground and Non-Ground Literals Preserve Completeness of Resolution, unpublished, 1994.
N.K. Zamov: On a Bound for the Complexity of Terms in the Resolution Method, Trudy Mat. Inst. Steklov 128, pp. 5–13, 1972.
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© 1997 Springer-Verlag Berlin Heidelberg
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de Nivelle, H. (1997). A classification of non-liftable orders for resolution. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_33
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DOI: https://doi.org/10.1007/3-540-63104-6_33
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