Related papers: Jacob's Ladder and Scientific Ontologies
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…
This comprehensive report distinguishes prior works by the cognitive functions they innovate. Many works claim an almost "human-like" cognitive capability in their world models. To evaluate these claims requires a proper grounding in first…
Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding…
Large language models (LLMs) have achieved remarkable progress in linguistic tasks, necessitating robust evaluation frameworks to understand their capabilities and limitations. Inspired by Feynman's principle of understanding through…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in modern educational, psychological, social and biological sciences. A key component of CDMs is a binary $Q$-matrix…
Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of…
"All men by nature desire to know," states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there…
Ontology alignment process is overwhelmingly cited in Knowledge Engineering as a key mechanism aimed at bypassing heterogeneity and reconciling various data sources, represented by ontologies, i.e., the the Semantic Web cornerstone. In such…
The traditional concept of knowledge is a justified true belief. The bulk of contemporary epistemology has focused primarily on that task of justification. Truth seems to be a quite obvious criterion-does the belief in question correspond…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section 2 presents the traditional…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…