2015/10/31 by Benjamin G. Rin, Benjamin Rin, Sean Walsh · 26 citations
Computer Science · Mathematics · #Accessibility relation #Algebra over a field #Algorithm #Calculus (dental) #Computability, Logic, AI Algorithms #Computer science #Description logic #Discrete mathematics #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Modal #Modal logic #Multimodal logic #Normal modal logic #Programming language #Pure mathematics #Realizability #S5 #Semantics (computer science) #math.LO #msc:03B40 #msc:03B45 #msc:03F55
paper · pdf · doi:10.1017/s1755020316000095
published in The Review of Symbolic Logic 9(4), 752-809 (Cambridge University Press) · Forthcoming in The Review of Symbolic Logic
arxiv created 2016/03/01 · openalex publication_date 2016/04/04 · arxiv updated 2016/04/13 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Abstract A semantics for quantified modal logic is presented that is based on Kleene’s notion of realizability. This semantics generalizes Flagg’s 1985 construction of a model of a modal version of Church’s Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church’s Thesis and a variant of a modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra’s generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott’s graph model (for the untyped lambda calculus) which witnesses the failure of the stability of nonidentity.