Related papers: Consistency Spaces
Fusing sentences containing disparate content is a remarkable human ability that helps create informative and succinct summaries. Such a simple task for humans has remained challenging for modern abstractive summarizers, substantially…
We prove that every lattice with more than one element has a proper congruence-preserving extension.
The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an adjunction to the category of Lattices. In this paper we will…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
Consistent belief functions represent collections of coherent or non-contradictory pieces of evidence, but most of all they are the counterparts of consistent knowledge bases in belief calculus. The use of consistent transformations cs[.]…
We consider overdetermined systems of difference equations for a single function $u$ which are consistent, and propose a general framework for their analysis. The integrability of such systems is defined as the existence of higher order…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
This paper examines how a notion of stable explanation developed elsewhere in Defeasible Logic can be expressed in the context of formal argumentation. With this done, we discuss the deontic meaning of this reconstruction and show how to…
Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…
We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.
A key problem in the description of language structure is to explain its contradictory properties of specificity and generality, the contrasting poles of formulaic prescription and generative productivity. I argue that this is possible if…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
Memory consistency models have been developed to specify what values may be returned by a read given that, in a distributed system, memory operations may only be partially ordered. Before this work, consistency models were defined…
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment.…
The role of consistent measures in the rigorous construction of nonabelian lattice theories is analized. General conditions that measures must fulfill to insure consistency, positivity and a mass gap are obtained. The impact of nongeneric…
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…
For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times…