Related papers: Conceptual Collectives
Concept discovery is one of the open problems in the interpretability literature that is important for bridging the gap between non-deep learning experts and model end-users. Among current formulations, concepts defines them by as a…
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…
Inspired by e-participation systems, in this paper we propose a new model to represent human debates and methods to obtain collective conclusions from them. This model overcomes drawbacks of existing approaches by allowing users to…
The theory introduced, presented and developed in this paper, is concerned with an enriched extension of the theory of Rough Sets pioneered by Zdzislaw Pawlak. The enrichment discussed here is in the sense of valuated categories as…
Using the previously developed concepts of semantic spacetime, I explore the interpretation of knowledge representations, and their structure, as a semantic system, within the framework of promise theory. By assigning interpretations to…
Formal Concept Analysis starts from a very basic data structure comprising objects and their attributes. Sometimes, however, it is beneficial to also define attributes of attributes, viz., meta-attributes. In this paper, we use Triadic…
We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context…
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce…
I take issue with AI formalizations of context, primarily the formalization by McCarthy and Buvac, that regard context as an undefined primitive whose formalization can be the same in many different kinds of AI tasks. In particular, any…
The number of academic papers being published is increasing exponentially in recent years, and recommending adequate citations to assist researchers in writing papers is a non-trivial task. Conventional approaches may not be optimal, as the…
We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice…
This paper provides a bundle perspective to contextuality by introducing new categories of contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The former approach generalizes earlier work on the…
By design, word embeddings are unable to model the dynamic nature of words' semantics, i.e., the property of words to correspond to potentially different meanings. To address this limitation, dozens of specialized meaning representation…
Formal Concept Analysis (FCA) offers several tools for qualitative data analysis. One possibility is to group objects that share common attributes together and get a concept lattice that describes the data. Quite often the size of this…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
Shapes of cognition is a new conceptual paradigm for the computational cognitive modeling of Language-Endowed Intelligent Agents (LEIAs). Shapes are remembered constellations of sensory, linguistic, conceptual, episodic, and procedural…
Relational concepts are indeed foundational to the structure of knowledge representation, as they facilitate the association between various entity concepts, allowing us to express and comprehend complex world knowledge. By expressing…
People acquire concepts through rich physical and social experiences and use them to understand and navigate the world. In contrast, large language models (LLMs), trained solely through next-token prediction on text, exhibit strikingly…