Type theory in human-like learning and inference

TL;DR

This paper proposes that type theory provides a formal framework for understanding human-like reasoning, especially in generating plausible hypotheses and reasoning at different abstraction levels, addressing a key gap in cognitive science models.

Contribution

It introduces the idea that type theory underpins human reasoning processes, supported by empirical observations on hypothesis generation and abstraction in cognition.

Findings

Humans generate reasonable hypotheses within constrained search spaces.

People distinguish between improbability and impossibility in reasoning.

Humans reason effectively across multiple levels of abstraction.

Abstract

Humans can generate reasonable answers to novel queries (Schulz, 2012): if I asked you what kind of food you want to eat for lunch, you would respond with a food, not a time. The thought that one would respond "After 4pm" to "What would you like to eat" is either a joke or a mistake, and seriously entertaining it as a lunch option would likely never happen in the first place. While understanding how people come up with new ideas, thoughts, explanations, and hypotheses that obey the basic constraints of a novel search space is of central importance to cognitive science, there is no agreed-on formal model for this kind of reasoning. We propose that a core component of any such reasoning system is a type theory: a formal imposition of structure on the kinds of computations an agent can perform, and how they're performed. We motivate this proposal with three empirical observations: adaptive constraints on learning and inference (i.e. generating reasonable hypotheses), how people draw distinctions between improbability and impossibility, and people's ability to reason about things at varying levels of abstraction.