Related papers: Topological Representation of Double Boolean Algeb…
The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP).…
Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic…
Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize…
The Crack Topology Score (CTS) is a recently proposed metric that focuses on evaluating the topological correctness of crack segmentation outputs. While pixel-wise metrics such as IoU or F1-score fail to capture structural validity, CTS…
Writing declarative models has numerous benefits, ranging from automated reasoning and correction of design-level properties before systems are built to automated testing and debugging of their implementations after they are built.…
Representation theorems are established for fixed points of adjoint functors between categories enriched in a small quantaloid. In a very general setting these results set up a common framework for representation theorems of concept…
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…
Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
Current research on qualitative spatial representation and reasoning mainly focuses on one single aspect of space. In real world applications, however, multiple spatial aspects are often involved simultaneously. This paper investigates…
Documents are core carriers of information and knowl-edge, with broad applications in finance, healthcare, and scientific research. Tables, as the main medium for structured data, encapsulate key information and are among the most critical…
Shape-Text matching is an important task of high-level shape understanding. Current methods mainly represent a 3D shape as multiple 2D rendered views, which obviously can not be understood well due to the structural ambiguity caused by…
Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to…
Dialog act (DA) recognition is a task that has been widely explored over the years. Recently, most approaches to the task explored different DNN architectures to combine the representations of the words in a segment and generate a segment…
The prosperity of deep learning contributes to the rapid progress in scene text detection. Among all the methods with convolutional networks, segmentation-based ones have drawn extensive attention due to their superiority in detecting text…
Case-based Reasoning (CBR) on high-dimensional and heterogeneous data is a trending yet challenging and computationally expensive task in the real world. A promising approach is to obtain low-dimensional hash codes representing cases and…
Reasoning in the 2-category Con of contexts, certain sketches for arithmetic universes (i.e. list arithmetic pretoposes; AUs), is shown to give rise to base-independent results of Grothendieck toposes, provided the base elementary topos has…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or…
A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable \omega-categorical relational structures have two algebraic counterparts for…