Related papers: Acyclic Comprehension is equal to Stratified Compr…
A previously found definition of complexity for spherically symmetric fluid distributions [1], is extended to axially symmetric static sources. In this case there are three different complexity factors, defined in terms of three structure…
A stratified space is a topological space equipped with a \emph{stratification}, which is a decomposition or partition of the topological space satisfying certain extra conditions. More recently, the notion of poset-stratified space, i.e.,…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of "category" for which equality…
The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite…
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. We consider the chain complex computing the homology groups…
To model is to represent. The threshold of decidability defines two epistemological choices: one model (or a finite number of models) suffices for representing the dynamics below the undecidable; above this threshold (defined as…
Interpretability is a pressing issue for decision systems. Many post hoc methods have been proposed to explain the predictions of a single machine learning model. However, business processes and decision systems are rarely centered around a…
Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…
Metaphorical meaning is not a flat mapping between concepts, but a complex cognitive phenomenon that integrates multiple levels of interpretation. In this paper, we propose a stratified model of metaphor processing that treats meaning as an…
Let E be a Frobenius category, let_E_ denote its stable category. The shift functor on_E_ induces a first shift functor on the category of acyclic complexes with entries in_E_ by pointwise application. Shifting a complex by 3 positions…
We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…
In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there…