The Undecidability of FO3 and the Calculus of Relations with Just One Binary Relation
Overview & Synopsis
The validity problem for first-order logic is a well-known undecidable problem. The undecidability also holds even for $\mathsf{FO}3$ and (equational formulas of) the calculus of relations. In this paper we tighten these undecidability results to the following: (1) $\mathsf{FO}3$ with just one binary relation is undecidable even without equality; and (2) the calculus of relations with just one character and with only composition, union, and complement is undecidable. Additionally we prove that the finite validity problem is also undecidable for the above two classes.
Indexed from repository: arXiv
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arxiv.org)
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Document Information
| Document Title | The Undecidability of FO3 and the Calculus of Relations with Just One Binary Relation |
|---|---|
| Author / Organization | Yoshiki Nakamura |
| Subject & Discipline | cs.LO |
| Categories | Computer Science & Mathematics |
| Publication Year | 2026 |
| License / Rights | arXiv Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
arXiv
(arxiv.org)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-778 |
| Original Source Link | Visit Source Page on arxiv.org » |