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arXiv · 2307.05046

On the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation

Yoshiki Nakamura
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Abstract

We introduce the $k$-variable-occurrence fragment, which is the set of terms having at most $k$ occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the $k$-variable-occurrence fragment using the finiteness of a monoid. As a case study, we prove that for Tarski's calculus of relations with bounded dot-dagger alternation (an analogy of quantifier alternation in first-order logic), the equational theory of the $k$-variable-occurrence fragment is decidable for each $k$.

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Yoshiki Nakamura. 2023-07-11. On the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation. https://doi.org/10.4230/lipics.mfcs.2023.69

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