2017/08/12 by David Fernández–Duque, Fernández-Duque, David, Petar Iliev +1
Computer Science · #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Multi-Agent Systems and Negotiation
paper · doi:10.48550/arxiv.1708.03770
openalex publication_date 2017/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator, and that the μ-calculus is exponentially more succinct than the equally-expressive tangled limit operator. These results hold for any class of spaces containing at least one crowded metric space or containing all spaces based on ordinals below ωω, with the usual limit operator. We also show that these results continue to hold even if we enrich the less succinct language with the universal modality.