Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic G. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel fr...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/282416 |
| Acceso en línea: | http://hdl.handle.net/10261/282416 https://api.elsevier.com/content/abstract/scopus_id/85127727932 |
| Access Level: | acceso abierto |
| Palabra clave: | Epistemic logics Many-valued modal logics Possibilistic semantics |
| Sumario: | In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic G. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames ⟨ W, π⟩ , where W is a non-empty set of worlds and π: W→ [0 , 1] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames ⟨ W, π⟩ where π satisfies the normalisation condition sup w∈Wπ(w) = 1. |
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