Related papers: Quasirationality and aspherical (pro-$p$)presentat…
The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of reasoning: probabilistic (i.e. purely observational), interventional, and counterfactual, that reflect the progressive sophistication of human thought regarding…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…
On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…
We consider the relative group presentation $\mathcal{P} = \langle G, \mathbf{x} | \mathbf{r} \rangle$ where $\mathbf{x} = \{ x \}$ and $\mathbf{r} = \{ xg_1 xg_2 xg_3 x^{-1} g_4 \}$. We show modulo a small number of exceptional cases…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.
Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…
Using half-integral weight modular forms we give a criterion for the existence of real quadratic $p$-rational fields. For $p=5$ we prove the existence of infinitely many real quadratic $p$-rational fields.
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
I discuss a special class of singularities obtained as a natural 4-dimensional generalization of the conical singularity. Such singularities (called quasiregular) are ruinous for the predictive force of general relativity, so one often…
In the field of Explainable Artificial Intelligence (XAI), counterfactual examples explain to a user the predictions of a trained decision model by indicating the modifications to be made to the instance so as to change its associated…
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L_w1,w(Q)-definability assumption may be dropped, and each class is determined by its model of dimension…
In the first section of the present work, we introduce the concept of pseudocomplementation for semirings and show semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…