Related papers: Mathematics, Recursion, and Universals in Human La…
How universal is human conceptual structure? The way concepts are organized in the human brain may reflect distinct features of cultural, historical, and environmental background in addition to properties universal to human cognition.…
The nature of the existence, revealed through Human cognitive system, has been evolving since the development of the languages. Part of such revelations were the geometrical forms and the numbers, whose beauty and order, wondrous and…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical…
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
Recent advances in neural network-based generative modeling have reignited the hopes in having computer systems capable of seamlessly conversing with humans and able to understand natural language. Neural architectures have been employed to…
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
In this paper we examine different meaning representations that are commonly used in different natural language applications today and discuss their limits, both in terms of the aspects of the natural language meaning they are modelling and…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Thousands of different forms (words) are associated with thousands of different meanings (concepts) in a language computer model. Reasonable agreement with reality is found for the number of languages in a family and the Hamming distances…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
Explanation constitutes an archetypal feature of human rationality, underpinning learning and generalisation, and representing one of the media supporting scientific discovery and communication. Due to the importance of explanations in…
Fairness for Machine Learning has received considerable attention, recently. Various mathematical formulations of fairness have been proposed, and it has been shown that it is impossible to satisfy all of them simultaneously. The literature…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
Reasoning is a key ability for an intelligent system. Large language models (LMs) achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect. For…
When faced with novel situations, people are able to marshal relevant considerations from a wide range of background knowledge and put these to use in inferences and predictions. What permits us to draw in globally relevant information and…