Work

On provability logics with linearly ordered modalities

Year: 2012

Type: preprint

Abstract: 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).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1210.4809

Authors: Beklemishev, Lev D., Fernández-Duque, David, Joosten, Joost J.

Institutions: National Research University Higher School of Economics, Russian Academy of Sciences, Lomonosov Moscow State University, Steklov Mathematical Institute, Universidad de Sevilla, Universitat de Barcelona

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Russian Foundation for Basic Research, Junta de Andalucía

OpenAlex ID: W2953189420

Cites: 15

Cited by: 4

Related to: 20