JUCS - Journal of Universal Computer Science 15(1): 63-71, doi: 10.3217/jucs-015-01-0063
Non-Denumerable Infinitary Modal Logic
expand article infoMax J. Cresswell‡
‡ University of Auckland, Auckland, New Zealand

Corresponding author: Max Cresswell ( m.cresswell@massey.ac.nz )

© Max Cresswell.
This article is freely available under the J.UCS Open Content License.
Citation: Cresswell MJ (2009) Non-Denumerable Infinitary Modal Logic. JUCS - Journal of Universal Computer Science 15(1): 63-71. https://doi.org/10.3217/jucs-015-01-0063
Open Access
Abstract
Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs ‹Γ, α› of sets Γ of well-formed formulae and well-formed formulae α. In this paper I show how a generalisation of the infinite cut-rule used by Segerberg and Goldblatt enables the removal of the limitation to denumerable sets of sequents.
Keywords
infinitary modal logic, canonical model, cut-rule, uniform substitution