Related papers: Class Algebra for Ontology Reasoning
This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
This article deals with OLAP systems based on multidimensional model. The conceptual model we provide, represents data through a constellation (multi-facts) composed of several multi-hierarchy dimensions. In this model, data are displayed…
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Efficiency and scalability are obstacles that have not yet received a viable response from the human activity recognition research community. This paper proposes an activity recognition method. The knowledge model is in the form of…
The relevance of machine learning (ML) in our daily lives is closely intertwined with its explainability. Explainability can allow end-users to have a transparent and humane reckoning of a ML scheme's capability and utility. It will also…
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…
This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
Retrieve information resources made by the machine processing may refer to multiple sources. A personal web as part of information resources in the Internet requires a feature that can be understood by computer machines. Therefore, in this…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
The predictive ability of database classifiers constructed with a network of interacting chemical oscillators is studied. Databases considered here are composed of records, where each record contains a number of parameters (predictors)…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
In distributed classification, each learner observes its environment and deduces a classifier. As a learner has only a local view of its environment, classifiers can be exchanged among the learners and integrated, or merged, to improve…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…
Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software…