The Only 3-Valued Logic Which Is a Natural Implication Expansion with the Variable-Sharing Property of Kleene’s Strong Logic
[EN] Let us refer by MK3 to Kleene’s strong 3-valued matrix. An implicative expansion of MK3 is natural if the conditional function defining it verifies modus ponens, assigns a designated value to a conditional whenever it assigns the same value to its antecedent and its consequent, and, finally, it...
| Authors: | , |
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| Format: | book part |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universidad de León |
| Repository: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/25671 |
| Online Access: | https://link.springer.com/chapter/10.1007/978-3-031-69940-5_10 https://hdl.handle.net/10612/25671 |
| Access Level: | Open access |
| Keyword: | Lógica Three-valued logics Kleene’s strong logic Natural conditionals Variable-sharing property Relevant logics 11 Lógica |
| Summary: | [EN] Let us refer by MK3 to Kleene’s strong 3-valued matrix. An implicative expansion of MK3 is natural if the conditional function defining it verifies modus ponens, assigns a designated value to a conditional whenever it assigns the same value to its antecedent and its consequent, and, finally, it coincides with the classical conditional function when restricted to the “classical” values t and f. Two are the main results of this paper. (1) It is proven that, from the viewpoint of functional strength, there is only one 3-valued natural implication expansion of MK3 with the variable-sharing property, the logic we dub L3^{VSP}. (2) It is shown that L3^{VSP} is a significant and strong logic that can be seen from different perspectives, one of them being to consider it an expansion of classical positive propositional logic. |
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