Related papers: Construction and Set Theory
This paper continues a research program on constructive investigations of non-commutative Ore localizations, initiated in our previous papers, and particularly touches the constructiveness of arithmetics within such localizations. Earlier…
In the several contexts such as combinatorial number theory, families of sets of positive integers closed under taking subsets have been investigated. Then it is sometimes useful to give bijections between the set of the one-sided infinite…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…