Abstract
It is often useful to simplify the resolution inference system by elimination of factoring. Factoring, however, cannot be ignored entirely without loosing completeness. This paper studies to what extent factoring is necessary to preserve it. We can show that it is sufficient to factorize only one of the two parent clauses of a resolvent. We apply this basic result to a class of well known refinements and describe for each rule which clause (the so called "selected parent") has at most to be factored.
We try to achieve the results in a transparent manner using only elementary notions of resolution theory, so that this note should be readable without detailed knowledge of resolution strategies.
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References
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Noll, H. (1980). A note on resolution: How to get rid of factoring without loosing completeness. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_20
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DOI: https://doi.org/10.1007/3-540-10009-1_20
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