Related papers: Functional Conceptual Substratum as a New Cognitiv…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…
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 provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the…
Knowledge is the most precious asset of humankind. People extract the experience from the data that provide for us the reality through the feelings. Generally speaking, it is possible to see the analogy of knowledge elaboration between…
It is quite exceptional, if it ever happens, that a new conceptual domain be built from scratch. Usually, it is developed and mastered in interaction, both positive and negative, with other more operational existing domains. Few reasoning…
Probabilistic conceptual network is a knowledge representation scheme designed for reasoning about concepts and categorical abstractions in utility-based categorization. The scheme combines the formalisms of abstraction and inheritance…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…
I think that the main reason why we do not understand the general principles of how knowledge works (and probably also the reason why we have not yet designed and built efficient machines capable of artificial intelligence), is not the…
Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To…
Lexical Semantics is concerned with how words encode mental representations of the world, i.e., concepts . We call this type of concepts, classification concepts . In this paper, we focus on Visual Semantics , namely on how humans build…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…