On the distributivity equation for uni-nullnorms

summary:A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized

The projective geometry of a group

We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize several results from preceding joint work with M. Kinyon (arXiv:0903.5441), which concerned abelian groups, to the case of general non-abelian groups. Most notably, pairs of subgroups parametrize torsor and semitorsor structures on the power set. The r\^ole of associative algebras and -pairs from loc. cit. is now taken by analogs of near-rings

A discussion on the origin of quantum probabilities

We study the origin of quantum probabilities as arising from non-boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).Comment: Improved versio

Doubled \alpha'-Geometry

We develop doubled-coordinate field theory to determine the \alpha' corrections to the massless sector of oriented bosonic closed string theory. Our key tool is a string current algebra of free left-handed bosons that makes O(D,D) T-duality manifest. While T-dualities are unchanged, diffeomorphisms and b-field gauge transformations receive corrections, with a gauge algebra given by an \alpha'-deformation of the duality-covariantized Courant bracket. The action is cubic in a double metric field, an unconstrained extension of the generalized metric that encodes the gravitational fields. Our approach provides a consistent truncation of string theory to massless fields with corrections that close at finite order in \alpha'.Comment: 54 pages, v2: version published in JHE

Layer by layer - Combining Monads

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence of a distributive law and gives a best approximant language. The running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, which results in a best approximant language structurally very similar to the probabilistic network specification language ProbNetKAT