TACL 2011 (Topology, Algebra, and Categories in Logic)
Sprache des Tagungstitel:
Commutative partially ordered monoids will be referred to as uninorms. Our aim is to investigate involutive uninorms. Our main question is the following: in an involutive FLe-algebra, how far its uninorm (or its algebraic structure, in general) is determined by its ?local behavior?, i.e., its underlying t-norm and t-conorm. An answer to this question is presented for a particular case on [0, 1] with t = f , which will illustrate our background idea. It says that the uninorm is determined uniquely by any of them, i.e., either by the t-norm or by the t-conorm . In fact, the t-norm and the t-conorm are determined by each other, in this case. Then, a natural question is how far we can extend this, and when the uninorm is determined uniquely? Our main goal is to give an answer to this question: Uniqueness is guaranteed and moreover, the uninorm is represented by the twin- rotation construction whenever the algebra is conic. To have a closer look at the situation, then we consider involutive FLe-algebras which are finite and linearly ordered. As a byproduct it follows that the logic IUL extended by the axiom t ? f does not have the finite model property.