Fuzzy logic with countable evaluated syntax revisited
In this paper, we revisit fuzzy logic with evaluated syntax Ev(L). An objection towards it is necessity to introduce logical constants (names of truth values) for all a is an element of [0, 1] into its language which makes it uncountable. Hajek has shown in his book "Metamathematics of fuzzy logic" that when seeing Ev(L) as RPL logic where the provability degree is an additional concept then we may confine only to rational logical constants. In this paper, we show that the same result can be obtained directly in Ev(L). The essential idea is to generalize slightly the concept of a complete fuzzy theory using the technique of Ev(L). (C) 2007 Elsevier B.V. All rights reserved.
evaluated syntax fuzzy logic in narrow sense lukasiewicz logic traditional syntax