Abstract
This paper proposes a bimodal logic with an additional modality (called the irreflexive modality), which corresponds semantically to the intersection of the accessibility relation and the inequality. First, we show that we can define, within this framework, several properties that are undefinable in the unimodal language; irreflexivity is one of such properties. Second, with respect to the frame expressivity, we compare our language with the unimodal language and another bimodal language with the difference operator that is studied by de Rijke. Finally, we give a Hilbert-style axiomatization of our logic and prove that certain familiar modal systems, such as S4 and S5, enjoy Kripke completeness in our language.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Japan Association for Philosophy of Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
