Predictive Modelling of Human Reasoning Using AGM Belief Revision

1 Introduction

Johnson-Laird, renown philosopher of language and reasoning, holds the view that humans exploit all the knowledge available to them to arrive at an inference, rather than apply formal logical rules. In response, the task of making formal rules of inference flexible to exceptions and tolerant of new information has been studied under the term nonmonotonic reasoning. A proponent [Oaksford and Chater, 2020] views reasoning as a social activity which, when formalised in classical true-false logic, is weakened by a lack of contextual knowledge and the limitation that background knowledge must be consistent. Both non-monotonic reasoning and belief change have been proposed as a better candidate for modelling human revision than classical logic. In the non-monotonic case, for example, suppose a reasoner has the knowledge that "Daisy is a Dodo", "Dodos are birds found around island nations in the Indian Ocean" and "birds fly'. Learning that "Dodos are flightless birds" presents evidence that causes the reasoner to withdraw the accepted knowledge that birds fly. On the other hand, belief change [Dubois et al., 2020] is the study of how old beliefs are changed to accommodate new information. While many forms of belief change have been studied, the relationship between belief revision and human reasoning is of primary interest in this work. The theory of belief revision extends classical logic with an approach to resolving conflict between a set of beliefs and newly learned information. For example, suppose a reasoner holds the belief that "A mystery box is behind door A or door B". This belief can be represented by the conjunction α ∨ β, where α and β indicates that the mystery box is behind door A and door B, respectively. Learning that door A opens to an empty room, causes the reasoner to revise their beliefs with ¬α, which means that the mystery box is not behind door A. To resolve the conflicting information, a reasoner may revise their beliefs by concluding that the mystery box is not behind door A, but behind door B, i.e. ¬α∧β. The broad objective of this project is to understand more about how humans revise their beliefs when presented with conflicting information. In previous work [Baker and Meyer, 2021], an output of Master's research, we surveyed English translations of the 8 Alchourr´on, G¨ardenfors and Makinson (AGM) [Alchourr´on et al., 1985] postulates of belief revision with human subjects. Half of the postulates were found agreeable with the subjects. A limitation of this work is that only one translation per postulate was used and that a comparison of the data for each postulate was not telling. Since humans are known to construct visual representations of their environment, it would be necessary to test each postulate repeatedly using varied material. Another limitation is that although the AGM postulates are a sound framework to examine the relationship between human reasoning and belief revision, the postulates are not considered complete. In recent literature, the AGM theory has been developed through the notions of relevance and independence, in which only the part of a belief set that is affected by the new information should be revised. Syntax splitting by Parikh [1999], considers this key idea concerning revising belief sets. In later work, Aravanis et al. [Aravanis et al., 2019] specified epistemic entrenchment models [G¨ardenfors and Makinson, 1988] and AGMstyle partial meet models for Parikh's relevance-sensitive axiom. Identified as a desirable property of knowledge representation and reasoning, syntax splitting has also been extended to the settings of iterated revision [Kern-Isberner and Brewka, 2017], non-monotonic reasoning [Kern-Isberner et al., 2020] and contraction [Haldimann et al., 2020], amongst others. While the revision theory has been extensively developed for enhancing logical inference, it is less clear whether humans find revision natural and useful. When incorporating new information into an existing belief set, a revision operation ranks the set of interpretations using total pre-orders [Delgrande et al., 2018]. The interpretations (beliefs) that are closest to the old set of beliefs are included in the revised set. We ask whether humans apply a similar ranking process to their beliefs when learning new information. In addition, a general population of human subjects may agree on a limited set of beliefs, especially when there is conflict. We propose to investigate whether humans find consistent beliefs important, and how conflicting information is resolved. The kinds of beliefs that human subjects retain or discard when learning new information will be studied, alongside the context of the situation. Furthermore, the AGM account of belief revision is based on logic, while cognitive models do not have a logical core. Instead, cognitive models use a representation of someone's intuition, knowledge, and interactions with the world. Johnson's [2010] is such a cognitive model that uses propositions to denote beliefs. The model makes deductions based on propositions, e.g "the car is parked outside", using if, and, or and not. We will draw a comparison between these two perspectives concerning their predictive power on human responses to resolving conflicting beliefs. A core requirement of this project is collecting data from human subjects. We propose to do this via two experiments: one to test how subjects identify information that is relevant in a given context and the other to test how subjects esteem beliefs after learning new information. The data from both surveys will be combined to produce a full representation of the subjects' beliefs. The variables of interest in the experiment are information relevance and information confidence. For each conversation, we will build two corresponding representations. The responses will first be analysed using standard statistical tests. Next, we will determine whether MMT can predict individual responses. Conveniently, MMT is a built-in model an open-source software platform called Cognitive Computation for Behavioural Reasoning Analysis (CCOBRA) 1 . The inferential power of MMT, via CCOBRA, will be compared to the logical inference of the 8 AGM postulates and desirable postulates for information relevance [Peppas and Williams, 2016]. In future, we will consider the impact of the broader work in the social science literature. A long-term goal of this work is to add significant features of revision to the existing MMT model on CCOBRA.

Ethical Statement

The ethical statement for this project can be accessed here: https://tinyurl.com/2p946xty.

Acknowledgments

Thanks to my supervisor, Prof. Thomas Meyer, for his mentorship and supervision of this project. Guidance on the cognitive science aspect was provided by Prof. Marco Ragni.