In this paper we consider the expansions of logics of a left-continuous t-norm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains defined over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over [0,1] ∩ ℚ where each truth-constant is interpreted in its corresponding rational truth-value. Finally, we study rational completeness results when we restrict ourselves to deductions between the so-called evaluated formulae. © Springer-Verlag 2009.
Esteva, F., Godo, L., Noguera, C. (2010). Expanding the propositional logic of a t-norm with truth-constants: Completeness results for rational semantics. SOFT COMPUTING, 14(3), 273-284 [10.1007/s00500-009-0402-8].
Expanding the propositional logic of a t-norm with truth-constants: Completeness results for rational semantics
Noguera C.
2010-01-01
Abstract
In this paper we consider the expansions of logics of a left-continuous t-norm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains defined over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over [0,1] ∩ ℚ where each truth-constant is interpreted in its corresponding rational truth-value. Finally, we study rational completeness results when we restrict ourselves to deductions between the so-called evaluated formulae. © Springer-Verlag 2009.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1200734