This paper presents an equivalence result between computability in the BSS model and in a suitable distributive category. It is proved that the class of functions R m ! R n (with n;m nite and R a commutative, ordered ring) computable in the BSS model, and the functions distributively computable over a natural distributive graph based on the operations of R coincide. Using this result, a new str...

We present a probabilistic approach to learning a Gaussian Process classifier in the presence of unlabeled data. Our approach involves a “null category noise model” (NCNM) inspired by ordered categorical noise models. The noise model reflects an assumption that the data density is lower between the class-conditional densities. We illustrate our approach on a toy problem and present comparative ...

These notes (still in draft form) arose from a challenge arising in the discussion of FMathL on the n-Category Café. I had claimed: “ For example, one can express with this naturally (and every mathematician immediately understands without the need for explanations) that ordered monoids are the objects in the intersection of Order and Monoid satisfying the compatibility relation R (suitably def...

Let us assume we are given a normal, normal, Gödel plane t. R. Sun’s construction of negative homeomorphisms was a milestone in fuzzy graph theory. We show that j is not homeomorphic to h. Moreover, recent developments in category theory [26] have raised the question of whether there exists a hyper-onto and unconditionally ordered group. The groundbreaking work of M. Thomas on categories was a ...

The Schützenberger product of monoids is a key tool for the algebraic treatment of language concatenation. In this paper we generalize the Schützenberger product to the level of monoids in an algebraic category D , leading to a uniform view of the corresponding constructions for monoids (Schützenberger), ordered monoids (Pin), idempotent semirings (Klíma and Polák) and algebras over a field (Re...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

We present a mathematical model for the cognitive operation of conceptual blending that aims at being uniform across different representation formalisms, while capturing relevant structure this operation. The takes its inspiration from amalgams as applied in case-based reasoning, but lifts them into category theory so to follow Joseph Goguen’s intuition mathematically precise characterisation r...

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...