First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties
This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit in...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/160427 |
| Acceso en línea: | http://hdl.handle.net/10261/160427 |
| Access Level: | acceso abierto |
| Palabra clave: | Truth-constants T-norm based fuzzy logics Residuated lattices Mathematical fuzzy logic First-order predicate non-classical logics Algebraic logic |
| Sumario: | This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind over(r, -) → φ, where φ has no additional truth-constants. © 2009 Elsevier B.V. All rights reserved. |
|---|