Gödel logics with monotone operators

Baaz, Matthias; Fasching, Oliver

doi:10.1016/j.fss.2011.04.012

Cited by 4 publications

(1 citation statement)

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“…• Finally, we mention the papers [2,18,3] where the authors study expansions of Gödel logic with a monotone unary operator • interpreted by monotone functions f : [0, 1] → [0, 1] satisfying, among other conditions, f (1) = 1. So, although they are very close to truthhedges, in general they are not necessarily requested to satisfy the other boundary condition f (0) = 0.…”

Section: Related Workmentioning

confidence: 99%

A logical approach to fuzzy truth hedges

Esteva

Godo

Noguera

2013

Information Sciences

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The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truthstressing 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.

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Section: Related Workmentioning

confidence: 99%