2012/10/17 by Lev D. Beklemishev, Beklemishev, Lev D., David Fernández–Duque +3
Computer Science · #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Multi-Agent Systems and Negotiation
paper · pdf · doi:10.48550/arxiv.1210.4809
openalex publication_date 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the logics GLP(Λ), a generalization of Japaridze's polymodal provability logic GLP(ω) where Λis any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP(ω) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP(Λ) and the decidability of GLP(Λ) for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment of GLP(Λ).