Belief Change as Propositional Update

Abstract

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non-conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model-theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction.The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logicbased formalizations of belief revision, syntactic and model-theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more "entrenched" than others in the face of contradiction are also discussed from the perspective of induction and theory revision.

Changing your mind

“…Likewise, computer programs for artificial intelligence have modeled such changes (de Kleer, 1986;Doyle, 1979), and measures have been developed to calculate the amount of change so that minimalism can be tested. These measures depend on counting all the beliefs that change their values (Elio & Pelletier, 1997;Harman, 1986;Hiddleston, 2005). For example, Elio and Pelletier wrote, "often this relies on counting the number of propositions whose truth values would change in one kind of revision versus another" (p. 426), and Harman's measure of change proposes that we "take the sum of the number of (explicit) new beliefs added plus the number of (explicit) old beliefs given up" (p. 59).…”

“…Minimalism predicts that you should give up the categorical proposition but that you should be less likely to do so than in the first sort of problem because there are two generalizations from which it yields a conclusion as opposed to only one generalization. In other words, the categorical proposition now has more inferential power, and so you should be more likely to retain it (Elio & Pelletier, 1997). If, for example, you deny that John followed the diet, you can no longer infer that he has a good supply of iron.…”

The Development of Counterfactual Reasoning in Belief Revision

“…This paradigm captures the essence of belief-revision in that there is a prior belief or understanding that must be adjusted to make it consistent with a new piece of information or conjecture. In contrast, some studies have used arbitrary relations that are previously unknown to the reasoners, such as "All Pylons had force fields around their cities" (Byrne & Walsh, 2005;Elio & Pelletier, 1997). With these arbitrary relations, adult reasoners either tend to reject the general statements or show no preferred strategy for revising beliefs that differentiate between the general and particular statements.…”

“…By the time people reach adulthood, counterfactual reasoning forms the basis of belief-revisioning (e.g., Dawes, 1964;Revlin, Bromage, & Van Ness, 1981;Stalnaker, 1998). Although belief revisioning has been studied among adults from different perspectives (e.g., Dieussaert, Schaeken, De Neys, & d'Ydewalle, 2000;Elio & Pelletier, 1997;Hadjichristidis, Handley, Sloman, Evans, Over, & Stevenson, 2007;Markovits & Schmeltzer, 2007;Politzer & Carles, 2001), little is known about the transition between the child's process of counterfactual reasoning and the adult form of belief revisioning. How do people normally absorb facts that conflict with their enduring beliefs and how do children adapt to this kind of situation?…”

Deductive reasoning from uncertain conditionals

“…Finally, there is a newly developped paradigm in psychology initiated by research in Artificial Intelligence which is highly relevant to the present topic, namely belief revision (Elio and Pelletier, 1997). It deals with how people accommodate a new piece of information that contradicts some of their previous beliefs.…”