JUCS - Journal of Universal Computer Science 6(1): 155-168, doi: 10.3217/jucs-006-01-0155
A Canonical Model Construction for Substructural Logics
expand article infoHajime Ishihara‡
‡ School of Information Science Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

Corresponding author: Hajime Ishihara ( ishihara@jaist.ac.jp )

© Hajime Ishihara.
This article is freely available under the J.UCS Open Content License.
Citation: Ishihara H (2000) A Canonical Model Construction for Substructural Logics. JUCS - Journal of Universal Computer Science 6(1): 155-168. https://doi.org/10.3217/jucs-006-01-0155
Open Access
Abstract
In this paper, we introduce a class of substructural logics, called normal substructural logics, which includes not only relevant logic, BCK logic, linear logic and the Lambek calculus but also weak logics with strict implication, and de ne Kripke- style semantics (Kripke frames and models) for normal substructural logics. Then we show a correspondence between axioms and properties on frames, and give a canonical construction of Kripke models for normal substructural logics. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.
Keywords
substructural logics, linear logic, relevant logics, strict implication, Kripke-type semantics, canonical model