A logical approach to fuzzy truth hedges
The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hájek's BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the exp...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Recursos: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::c8cda8c2c379417ceaecc7cba11f2b75 |
| Acesso em linha: | http://hdl.handle.net/10261/132598 |
| Access Level: | acceso abierto |
| Palavra-chave: | Mathematical fuzzy logic Truth hedges Standard completeness t-Norm based logics |
| Resumo: | The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hájek's BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages: (i) they preserve the standard completeness properties of the original logic and (ii) any subdiagonal (resp. superdiagonal) non-decreasing function on [0, 1] preserving 0 and 1 is a sound interpretation of the truth-stresser (resp. depresser) connectives. Hence, these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense. © 2013 Elsevier Inc. All rights reserved. |
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