Related papers: Conceptua: Institutions in a Topos
The explicit relationship among perception, communication, and design is being discussed in some detail, in order to relate it to characteristic details of the modeling of the world which defines the scientific and artistic activities of…
Formalizing creativity-related concepts has been a long-term goal of Computational Creativity. To the same end, we explore Formal Learning Theory in the context of creativity. We provide an introduction to the main concepts of this…
We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results…
We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct…
Data is always at the center of the theoretical development and investigation of the applicability of formal concept analysis. It is therefore not surprising that a large number of data sets are repeatedly used in scholarly articles and…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
In the eyes of a rationalist like Descartes or Spinoza, human reasoning is flawless, marching toward uncovering ultimate truth. A few centuries later, however, culminating in the work of Kahneman and Tversky, human reasoning was portrayed…
The problem of defining and locating free will (FW) in physics is studied. On basis of logical paradoxes, we argue that FW has a meta-theoretic character, like the concept of truth in Tarski's undefinability theorem. Free will exists…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
In the concluding remarks of Ontological Promiscuity Hobbs (1985) made what we believe to be a very insightful observation: given that semantics is an attempt at specifying the relation between language and the world, if "one can assume a…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
This paper introduces several fundamental concepts in information theory from the perspective of their origins in engineering. Understanding such concepts is important in neuroscience for two reasons. Simply applying formulae from…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
I discuss several aspects of information theory and its relationship to physics and neuroscience. The unifying thread of this somewhat chaotic essay is the concept of Kolmogorov or algorithmic complexity (Kolmogorov Complexity, for short).…
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…
Compositionality is believed to be fundamental to intelligence. In humans, it underlies the structure of thought, language, and higher-level reasoning. In AI, compositional representations can enable a powerful form of out-of-distribution…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…