Abstract
We show that negation elimination is decidable for linear complement problems interpreted in \(T(\mathcal{F})/{ = _{AC}},\), where AC is a set of associative and commutative axioms. For this, we present a system of rewrite rules that transforms any linear complement problem into a simple formula, and we give a test for deciding whether a simple formula is satisfiable in \(T(\mathcal{F})/{ = _{AC}}\) or not. This test serves as a basis for the development of a negation elimination algorithm.
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Fernández, M. (1993). AC complement problems: Satisfiability and negation elimination. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_27
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DOI: https://doi.org/10.1007/978-3-662-21551-7_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56868-1
Online ISBN: 978-3-662-21551-7
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