TOPOLOGY AND MODALITY: THE TOPOLOGICAL INTERPRETATION OF FIRST-ORDER MODAL LOGIC
β Scribed by Awodey, Steve (author);Kishida, Kohei (author)
- Book ID
- 111916567
- Publisher
- Cambridge University Press
- Year
- 2008
- Tongue
- English
- Weight
- 242 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1755-0203
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## Abstract We study modal logics based on neighbourhood semantics using methods and theorems having their origin in topological model theory. We thus obtain general results concerning completeness of modal logics based on neighbourhood semantics as well as the relationship between neighbourhood an
We consider first order modal logic C firstly defined by Carnap in "Meaning and Necessity" [1]. We prove elimination of nested modalities for this logic, which gives additionally the Skolem-LΓΆwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0 .