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Guarded Negation Transitive Closure Logic
[Submitted on 25 Jan 2025 (v1), last revised 18 Jul 2026 (this v · 2025-01-26 · via cs.DB updates on arXiv.org

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Abstract:We study the guarded negation fragment of transitive closure logic (GNTC). We show that the satisfiability problem for GNTC is 2ExpTime-complete, by establishing the following reductions: (i) a polynomial-time reduction from the satisfiability problem for GNTC to the satisfiability problem for the unary negation fragment UNTC of GNTC, and (ii) a direct exponential-time reduction from the satisfiability problem for UNTC to the non-emptiness problem for 2-way alternating parity tree automata. Furthermore, we show that the model checking problem for GNTC is $\mathsf{P}^{\mathsf{NP}[\mathcal{O}(\log^2 n)]}$-complete in combined complexity. Our result implies $\mathsf{P}^{\mathsf{NP}[\mathcal{O}(\log^2 n)]}$-completeness for both UNTC and $\mathrm{UNFO}^{\mathrm{reg}}$, which were left open in previous works.

Submission history

From: Yoshiki Nakamura [view email]
[v1] Sat, 25 Jan 2025 19:00:51 UTC (67 KB)
[v2] Thu, 27 Mar 2025 17:44:35 UTC (71 KB)
[v3] Sat, 16 May 2026 11:44:17 UTC (361 KB)
[v4] Sat, 18 Jul 2026 02:13:14 UTC (364 KB)