Scope of Real Beliefs in Belief Revision

Scope of Real Beliefs in Belief Revision Alexander B. Swan (swan@psych.ucsb.edu) Alexandra Y. Chambers (chambers@psych.ucsb.edu) Russell Revlin (revlin@psych.ucsb.edu) Department of Psychological and Brain Sciences, University of California, Santa Barbara Santa Barbara, CA 93106-9660 USA Abstract The present study examines the decisions made by reasoners when they are asked to revise their beliefs in the face of new, counterfactual information. Participants indicated the Scope (the degree of set inclusion) of semantic generalizations about real categories in a Pretest. In subsequent experiments, these Scope values were used to predict the willingness of participants to retain statements in their existing knowledge sets. When those sets were logically compatible with a Modus Tollens (MT) structure, participants were more likely to retain the general statements, but not when the sets were logically compatible with a Modus Ponens (MP) structure. However, the MP retention rates increased when locatives were added to the generalizations. These findings are inconsistent with several prevailing proposals of belief revision but do support the concept of belief revision as following Possible Worlds logic. Keywords: belief revision; counterfactual reasoning; scope. Introduction The process of belief revision is known by many terms (e.g., belief updating, belief change or belief dynamics). Simply put, belief revision involves the possibility of changing a previously held belief in light of new and assumed true information. At its very basic level, this involves updating knowledge and resolving inconsistencies within a pre-existing knowledge structure. True belief revision must involve commitment to true beliefs. The earliest belief revision studies employed dictionary definitions without proper verification that those definitions had merit or that the students were committed to those definitions (Revlis & Hayes, 1972). Later studies examined belief revision with artificial categories or groups, of which a participant might have had no previous knowledge (e.g., Byrne & Walsh, 2002; Elio & Pelletier, 1997; Politzer & Carles, 2001; Revlin, Cate, & Rouss, 2001). Revlin, Calvillo, and Ballard (2005) specifically created a fantasy world with Lego figures and various arbitrary rules about knights and kings (see also Van Hoeck, Revlin, Dieussaert, & Schaeken, 2012). In each of these cases, real beliefs were not tested. It is difficult to assess the process of belief updating when the epistemic system is limited to arbitrary or unverified knowledge. The findings from such studies have supported conflicting theoretical treatments (e.g., Byrne & Walsh, 2002; Wolf, Rieger, & Knauff, 2012; Revlin et al., 2001; Revlis & Hayes, 1972). The focus of the present study is to identify the basic cognitive processes in true belief revision while still employing an established paradigm. A basic paradigm for studying natural belief revision has been borrowed from the philosophical treatment of belief- contravening problems (Rescher, 1964): It consists of a set of beliefs that are relevant to a counterfactual assumption, whose introduction requires a revision of the belief set. For example, (1a) All whales are mammals (1b) This creature is not a mammal (1c) This creature is not a whale (1d) Assume that this creature is a whale A typical adult reasoner with the current knowledge of statements (1a-1c) would appreciate the inherent consistency of these statements. This collection of statements follows the logical form of Modus Tollens (MT; p  q, ~q, ∴ ~p). However, if someone is faced with statement (1d), an inconsistency is introduced to the knowledge structure and the revision process requires the reestablishment of a consistent epistemic set that entails the retention of (1d). To accomplish this, the reasoner notices that statement (1d) is in direct contradiction to statement (1c), which can be easily eliminated. However, there is a larger issue. The remaining statements (1a & 1b) jointly create a contradiction with (1d). To resolve this inconsistency, a choice must now be made: Does the individual accept statement (1a), retaining the previously held belief that all whales are mammals, and that it cannot be true that there is an creature that is classified as a whale that is not a mammal? Or does the individual accept statement (1b), and claim that it could be true that there are creatures classified as whales that are not mammals? The revision process requires the elimination of one of the two statements. Either path is equally logical, although standard logic fails to encourage a preference, only indicating to the reasoner that there is an inconsistency (Chisholm, 1946). While an individual can reject both statements, the goal is generally to retain the maximum number of statements that already exist within the epistemic set. A second logical form typically used in belief-contravening problems is that of Modus Ponens (MP; p  q, p, ∴ q), illustrated in (2) below: (2a) All whales are mammals (2b) This creature is a whale (2c) This creature is a mammal (2d) Assume that this creature is not a mammal