# Modeling Arbitrarily Applicable Relational Responding with the Non-Axiomatic Reasoning System: A Machine Psychology Approach

arXiv: https://arxiv.org/abs/2503.00611 · HTML: https://mlsanity.com/paper/2503.00611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Machine Psychology: Integrating Operant Conditioning with the Non-Axiomatic Reasoning System for Advancing Artificial General Intelligence Research](https://mlsanity.com/paper/2405.19498/) (2024)
- [Functional Equivalence with NARS](https://mlsanity.com/paper/2405.03340/) (2024)
- [Inductive Learning of Robot Task Knowledge from Raw Data and Online Expert Feedback](https://mlsanity.com/paper/2501.07507/) (2025)

## Abstract (arXiv)

Arbitrarily Applicable Relational Responding (AARR) is a cornerstone of human language and reasoning, referring to the learned ability to relate symbols in flexible, context-dependent ways. In this paper, we present a novel theoretical approach for modeling AARR within an artificial intelligence framework using the Non-Axiomatic Reasoning System (NARS). NARS is an adaptive reasoning system designed for learning under uncertainty. By integrating principles from Relational Frame Theory - the behavioral psychology account of AARR - with the reasoning mechanisms of NARS, we conceptually demonstrate how key properties of AARR (mutual entailment, combinatorial entailment, and transformation of stimulus functions) can emerge from the inference rules and memory structures of NARS. Two theoretical experiments illustrate this approach: one modeling stimulus equivalence and transfer of function, and another modeling complex relational networks involving opposition frames. In both cases, the system logically demonstrates the derivation of untrained relations and context-sensitive transformations of stimulus significance, mirroring established human cognitive phenomena. These results suggest that AARR - long considered uniquely human - can be conceptually captured by suitably designed AI systems, highlighting the value of integrating behavioral science insights into artificial general intelligence (AGI) research.