Two Neighborhood Semantics for Subintuitionistic Logics
This investigation is concerned with weak subintuitionistic logics interpreted over neighborhood models introduced by the authors in 2016. The two types of neighborhood semantics introduced in that article are compared and their relationship is clarified. Thereby modal companions for various logics are recognized. Specifically, a logic is found which has basic monotonic logic with necessitation as its modal companion. Many of the extensions of the basic logics are discussed and characterized.
KeywordsIntuitionistic logic Subintuitionistic logic Modal companions Neighborhood models
This paper greatly profited from the remarks of an anonymous referee who read the paper very carefully. Many points were clarified and readability has improved strongly. The second author expresses thanks for the financial support of the project number 95012990 of the Iran National Science Foundation (INSF) as a post-doc researcher at school of mathematics, statistics and computer science of university of Tehran.
- 3.Hansen, H.H.: Monotonic modal logics. Master thesis, University of Amsterdam (2003)Google Scholar