Using Theory Resolution to Simplify Interpreted Formulae
Loveland & Shostak (1980) gave an algorithm for converting a decision procedure for ground formulae in a first-order theory to a simplifier for such formulae. The algorithm is supposed to produce a simplest clause set among all formulae built from atoms of the original formula. The method proceeds by submitting all clauses that consist solely of atoms of the original formula to the decision procedure. The valid ones are added to the formula and then Quine’s algorithm of iterated consensus (Quine 1959) is applied. In this paper it is shown that this method does not meet the requirement of producing a simplest semantic equivalent. Furthermore we show that theory resolution can be used to extend Quine’s method to an algorithm that really accomplishes the task of simplifying interpreted formulae.
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- Loveland, D.W. & Shostak, R.E. (1980). Simplifying Interpreted Formulas. In: W. Bibel & R. Kowalski (Eds.): Proc. of 5th Conference on Automated Deduction, Les Arcs. Springer LNCS 87, 97 – 109Google Scholar