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arXiv · 2303.13257

Equational Theorem Proving for Clauses over Strings

Dohan Kim
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Abstract

Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus with strings and present an equational theorem proving framework for clauses over strings. It provides a saturation procedure for clauses over strings and show that the proposed superposition calculus with contraction rules is refutationally complete. This paper also presents a new decision procedure for word problems over strings w.r.t. a set of conditional equations R over strings if R can be finitely saturated under the proposed inference system.

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Dohan Kim. 2023-03-23. Equational Theorem Proving for Clauses over Strings. https://doi.org/10.1017/s0960129524000112

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