25 documents found, page 1 of 3
A Theory of Marginal and Large Difference
Dinis, Bruno; Jacinto, BrunoWe propose a new theory based on the notions of marginal and large difference which has natural models in the context of nonstandard mathematics. We introduce the notion of finite marginality and show a representation result which ensures, for finitely marginal countable models, the existence of a homomorphism of the structure of marginal and large difference into a nonstandard model of the natural numbers, and...
Towards an enumeration of finite common meadows
Dinis, Bruno; Dias, JoãoCommon meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term a which is absorbent for addition. We study the problem of enumerating all finite common meadows of order n (that is, common meadows with n elements). This problem turns out to be d...
Strolling through common meadows
Dinis, Bruno; Dias, JoãoThis paper establishes a connection between rings, lattices and common meadows. Meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. Common meadows are meadows that introduce, as the inverse of zero, an error term a which is absorbent for addition. We show that common meadows a...
Flexible Involutive Meadows
Dinis, Bruno; Bottazzi, EmanueleWe investigate a notion of inverse for neutrices inspired by Van den Berg and Koudjeti’s decomposition of a neutrix as the product of a real number and an idempotent neutrix. We end up with an algebraic structure that can be characterized axiomatically and generalizes involutive meadows. The latter are algebraic structures where the inverse for multiplication is a total operation. As it turns out, the structure...
Counterparts as Near-Equals
Dinis, Bruno; Jacinto, BrunoThis paper offers an account of the ship of Theseus paradox along the lines of the so-called nonstandard primitivism about vagueness. This account is inspired by a model of the ship of Theseus paradox offered by Dinis that considers near-equality, in the context of Nonstandard Analysis, as the proper way to model the `same as' relation. The output is a class of models which unifies the semantic account of vague...
On definable Skolem functions and trichotomy
Dinis, Bruno; Edmundo, MarioIn this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many elements from the prime model, a union of finitely many trivial points each defined over ∅ and finitely many open intervals each a union of a ∅-definable family of group-intervals with fixed positive elements.
Flasque meadows
Dinis, Bruno; Dias, JoaoIn analogy with flasque sheaves, we introduce the notion of flasque meadow as a common meadow where the transition maps are all surjective. We study some properties of flasque meadows and illustrate them with several examples and counterexamples.
Elements for Weighted Answer-Set Programming
Dinis, Bruno; Coelho, Francisco; Abreu, Salvador; Seipel, DietmarLogic programs, more specifically, answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (e.g. probabilities) of an answer-set program to its stable models, and from there to events (defined as sets of atoms) in a dataset over the program’s domain. We propose a novel approach which is algebraic in the sense tha...
Effective Metastability for a Method of Alternating Resolvents
Dinis, Bruno; Pinto, PedroA generalized method of alternating resolvents was introduced by Boikanyo and Morosanu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two different sets of conditions. As a consequence we obtain effective rates of metastability (in the sense of Terence Tao) and quasi-rates of asymptotic regularity. Furthermore, we b...
Assemblies as Semigroups
Dardano, Ulderico; Dinis, Bruno; Terzo, GiuseppinaIn this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.