Categorical approaches to non-commutative fuzzy logic

Categorical approaches to non-commutative fuzzy logic

In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a noncommutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of ...

Categorical semantics of non-commutative logic

Previous work [9, 1, 10] was devoted to proof nets and sequent calculus for NL. Here we study the categorical semantics of NL. One can say that proof nets constitute already a semantics of proofs of NL, but on one hand the extension to non-multiplicative connectives is delicate (boxes) and on the other hand one would like to have a semantics that is more general than syntax (correctness) and cl...

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

Two Approaches to Non-Commutative Geometry

Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)—to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. ∗Support...

Categorical Logic Categorical Logic