Related papers: Pinning quasi orders with their endomorphisms
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level…
Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…
We study the fair allocation of indivisible items under relevance constraints, where each agent has a set of relevant items and can only receive items that are relevant to them. While the relevance constraint has been studied in recent…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
Many applications, e.g., Web service composition, complex system design, team formation, etc., rely on methods for identifying collections of objects or entities satisfying some functional requirement. Among the collections that satisfy the…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to…
This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
The principle that 'the brand effect is attractive' underlies preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly develop a general framework…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories…