Abstract

We propose an extension of rewriting techniques to derive inclusion relations $a \subseteq b$ between terms built from monotonic operators. Instead of using only a rewriting relation $\REa$ and rewriting $a$ to $b$, we use another rewriting relation $\REb$ as well and seek a common expression $c$ such that $a \REa^* c$ and $b \REb^* c$. Each component of the bi-rewriting system $\pair{\REa}{\REb}$ is allowed to be a subset of the corresponding inclusion $\subseteq$ or $\superseteq$. In order to assure the decidability and completeness of the proof procedure we study the commutativity of $\REa$ and $\REb$. We also extend the existing techniques of rewriting modulo equalities to bi-rewriting modulo a set of inclusions. We present the canonical bi-rewriting system corresponding to the theory of non-distributive lattices.

Citations