Belief-Logic Conflict Resolution 1 Running Head: BELIEF-LOGIC CONFLICT RESOLUTION Belief-Logic Conflict Resolution in Syllogistic Reasoning: Inspection-Time Evidence for a Parallel-Process Model

An experiment is reported examining dual-process models of belief bias in syllogistic reasoning using a problem complexity manipulation and an inspection-time method to monitor processing latencies for premises and conclusions. Endorsement rates indicated increased belief-bias on complex problems, a finding that runs counter to the “belief-first” selective scrutiny model, but which is consistent with other theories, including “reasoning first” and “parallel-process” models. Inspection-time data revealed a number of effects that, again, arbitrated against the selective scrutiny model. The most striking inspection-time result was an interaction between logic and belief on premise processing times, whereby belief-logic conflict problems promoted increased latencies relative to non-conflict problems. This finding challenges belieffirst and reasoning-first models, but is directly predicted by parallel-process models, which assume that the outputs of simultaneous heuristic and analytic processing streams lead to an awareness of belief-logic conflicts than then require timeconsuming resolution. Belief-Logic Conflict Resolution 3 Belief-Logic Conflict Resolution in Syllogistic Reasoning: Inspection-Time Evidence for a Parallel-Process Model Belief bias in reasoning is a non-logical tendency to accept conclusions that are compatible with beliefs more frequently than conclusions that contradict beliefs. The bias is more pronounced on invalid than valid problems, giving rise to a logic by belief interaction in conclusion-endorsement rates that has been studied extensively since it was established by Evans, Barston, and Pollard (1983). Contemporary theories of belief bias are couched within a dual-process framework (e.g., Evans, 2006; Stanovich, 2004) which characterises the phenomenon as arising from the interplay between belief-based “heuristic” processes that are rapid, associative and implicit, and logic-based “analytic” processes that are slow, sequential, explicit, and constrained by working memory limitations. The belief-bias effect suggests that heuristic processes may often dominate over analytic processes in cueing responses. Dual-process theories of belief bias have gained support from a wide range of sources, including: neuroimaging studies demonstrating the neurological differentiation of logic-based and belief-based responding (Goel & Dolan, 2003); research indicating how resolving belief-logic conflicts in favour of logic declines with age (Gilinsky & Judd, 1994); and studies demonstrating how people high in general intelligence are better able to resist belief bias (Stanovich & West, 1997). Despite the support for a general dual-process view of belief bias, however, little consensus exists as to which specific dual-process theory of belief bias is best able to capture the full range of available data. Indeed, all current theories gain some support, yet differ markedly in their assumptions about the sequencing of heuristic and analytic operations. The primary goal of the present research was to realise a syllogismBelief-Logic Conflict Resolution 4 complexity manipulation so as to examine predictions deriving from three distinct classes of belief-bias theory that we refer to as “belief-first”, “reasoning-first” and “parallel-process” models (we are grateful to Jonathan Evans, personal communication, for this characterisation of theories). Our research was also motivated by a secondary goal, which was to employ an inspection-time measure of processing to clarify how heuristic and analytic processes compete to determine responding. To this end, we developed a computer-based, mouse-contingent display technique to monitor problem inspection-times for syllogism components (cf. Roberts & Newton, 2001; Schroyens, Schaeken, Fias, & d'Ydewalle, 2000). We know of two previous belief-bias studies that involved response-time measures (i.e., Ball, Phillips, Wade, & Quayle, 2006; Thompson, Striemer, Reikoff, Gunter, & Campbell’s, 2003). These studies revealed some inconsistencies in observed effects, although they converged in showing that people spend more time processing syllogisms with believable conclusions. Both studies, however, had limitations that the present research aimed to overcome. In Ball et al.’s (2006) experiment conclusion validity was confounded with premise configuration such that valid conclusions were always presented with “Some A are B; No B are C” premises, whilst invalid conclusions were always presented with “No A are B, Some B are C” premises. Thompson et al.’s experiment involved a latency measure that simply recorded the overall time to evaluate conclusions. This rather coarse measure may have obscured more subtle chronometric evidence that might emerge from a finergrained examination of the locus of processing effort on premise and conclusion components. Moreover, Thompson et al. failed to examine latency data for violations of normality, yet such violations are common in chronometric data and can impact severely on test validity (Ball, Lucas, Miles, & Gale, 2003). Belief-Logic Conflict Resolution 5 Belief-First Models Belief-first theories come in two distinct flavours, referred to by Evans (in press) as pre-emptive conflict resolution and default-interventionist models. An example of the former is the selective scrutiny model (Evans et al., 1983). This assumes that believable conclusions are responded to heuristically (and simply accepted), whereas unbelievable conclusions motivate more rigorous analytic processing directed at testing conclusion validity. Evans and Pollard (1990) found support for the selective scrutiny model by demonstrating how a complexity manipulation affected discrimination of true from false conclusions, but not the magnitude of the belief-bias effect. This makes sense under the selective scrutiny model (Evans, Newstead, & Byrne, 1993), since belief is processed first, followed by an attempt at logical analysis; if analytic processing fails (more likely with complex problems) then random errors will ensue. Evans and Pollard’s (1990) apparent failure to find increased belief bias with complex problems has, however, been questioned by Klauer, Musch, and Naumer (2000), who note that the decreased variance observed in responses to such problems actually suggests that “the relative impact of belief was larger in the groups with complex problems” (Klauer et al., 2000, p. 856, emphasis added). This proposal underlines the need for further research exploring how complexity influences belief bias. It is also important to consider what the selective scrutiny model might predict concerning inspection times. Presumably, the premises of unbelievable conclusions should be inspected for longer, since reasoners are more likely to engage in analytic processing for these than believable ones (Evans, 2007). Such increased processing of unbelievable syllogisms should arise irrespective of problem complexity. Default-interventionist models also assume an early influence of beliefs, Belief-Logic Conflict Resolution 6 viewing heuristically-cued “default” responses as being either supported or inhibited by subsequent analytic processing. For example, the selective processing model (Evans, 2000, 2007; Evans, Handley, & Harper, 2001), proposes that the default heuristic response is to accept believable and reject unbelievable conclusions, which explains why belief-bias arises on both valid and invalid problems. If analytic processes intervene, however, then it is assumed that such processes will try to construct only a single mental model of the premises. But this analytic component of reasoning is itself biased by conclusion believability, such that a search is initiated for a confirming model when the conclusion is believable and for a falsifying model when the conclusion is unbelievable (cf. Klauer et al., 2000). These assumptions readily explain the increased belief-bias seen on invalid syllogisms since both confirming and falsifying models exist. The selective processing model also explains the increased belief bias and decreased logical performance that was predicted and observed under speededresponse instructions by Evans and Curtis-Holmes (2005), since these effects would be a natural consequence of elevations in default, heuristic responding. Presumably, too, any effect of problem complexity on the magnitude of belief bias would likewise arise through increased recourse to default responding and diminished analytic intervention (i.e., there should be an increase in belief-bias and a decrease in logicbased responding). As for inspection-time predictions, the selective-processing model differs from the selective scrutiny model and does not predict that people will take longer to process unbelievable conclusions, since analytic intervention is just as likely for believable as unbelievable conclusions (Evans, 2007). Reasoning-First Models Reasoning-first models of belief bias propose that people strive to reason Belief-Logic Conflict Resolution 7 analytically, only falling back on heuristic responding when analytic processing fails. Such accounts have been referred to as computational escape hatch models (Ball & Quayle, 2000; Stanovich & West, 2000). A recent example is Quayle and Ball’s (2000) metacognitive uncertainty theory, which is closely allied to the misinterpreted necessity model proposed by Evans et al. (1983). Both accounts emphasise uncertainty as a determinant of belief-bias, with people producing a belief-based response when a conclusion is possible but not necessitated by the premises (i.e., when conclusions are indeterminate). The difference between the metacognitive uncertainty theory and the misinterpreted necessity model resides primarily in the weight that the former places on limited working-memory capacity as a cause of uncertainty. In terms of conclusion-acceptance rates, these reasoning-first theories predict that problem complexity should increase belief-bias (e.g., by further increasing uncertainty) and decrease logical responding. As for inspection times, reasoning-first models would predict more rapid responding with valid conclusions irrespective of problem complexity, since reasoners should generally be more confident with valid than invalid syllogisms. Parallel-Process Models A third way in which heuristic and analytic reasoning processes may operate is as parallel processing streams. The best example of such a model is arguably Sloman’s (1996, 2002) theory, which posits parallel “associative” (heuristic) and “rule-based” (analytic) systems. Sloman proposes that both systems will usually try to generate a response, and that the rule-based system has some capacity to suppress the associative system, although the associative system always “has its opinion heard” and can defuse a rule-based response. This model would lead to response conflicts Belief-Logic Conflict Resolution 8 whenever belief-based (associative) and logical (rule-based) processes cue different outputs. These conflicts, moreover, would need to be resolved, perhaps according to some mechanism favouring logic with a certain probability (see Evans, in press, for a mathematical instantiation of such a mechanism that captures standard belief-bias effects). Within a parallel-process model, problem complexity would presumably shift the balance of responding toward beliefs and away from logic since the analytic processing stream would have difficulty in delivering an output. Inspection-time predictions for parallel-process models of belief bias are unique, since people should be “aware” of the conflict between belief-based and logic-based responses cued by the two systems (we are grateful to Jonathan Evans, personal communication, for alerting us to this). Such conflict awareness would arise for valid-unbelievable and invalid-believable syllogisms, and the need for conflict resolution should lead to increased processing times for these problems relative to those where belief and logic deliver equivalent responses (valid-believable and invalid-unbelievable syllogisms). Method Participants Forty-eight undergraduates aged between 18 and 55 from the University of Derby received course credit for participation. None had received prior instruction concerning the psychology of reasoning. All were tested individually. Design A 2 x 2 x 2 x 2 repeated-measures design was used that manipulated figural complexity (AB-BC vs. BA-CB), mood (IEO vs. EIO), logic (valid vs. invalid conclusions) and belief (believable vs. unbelievable conclusions). To control for biases linked to preferred conclusion orders (A-C or C-A), problems were collapsed Belief-Logic Conflict Resolution 9 across mood in all analyses. The use of the BA-CB figure to produce complex problems was based on evidence that people find this figure harder to process because demanding mental operations are required to ensure that middle terms of premises are represented contiguously (Espino, Santamaría, & Garcìa-Madruga, 2000, JohnsonLaird & Bara, 1984; Stupple & Ball, 2005, 2007). Dependent measures were conclusion-acceptance rates and inspection times for premises and conclusions. Materials and Procedure Participants received 16 target syllogisms (eight AB-BC; eight BA-CB) in IEO and EIO moods, preceded by four practice syllogisms in AEA, III, IAI and AEE moods. Belief-oriented contents drew on those employed by Quayle and Ball (2000). Unbelievable conclusions were definitionally false (e.g., Some cats are not animals), and believable conclusions were definitionally true (e.g., Some animals are not cats). Invalid conclusions were indeterminate (consistent with premises but not necessitated by them). For each figure there were equal numbers of valid and invalid problems and believable and unbelievable conclusions. Presentation order of target syllogisms was counterbalanced using a balanced Latin square design, with thematic contents systematically rotated through the 16 problems. Authorware 5.1 on a PC was used to present problems and standard instructions (cf. Ball et al., 2006) and to record responses and inspection times for problem regions. Participants were informed that for each problem there would be masked statements labelled “Premise 1”, “Premise 2” and “Conclusion”, and that a single click of the mouse on masked areas would reveal the underlying statement until the mouse was moved from that area. Participants could revisit masked areas as often as they wished before registering a “yes” or “no” decision as to the conclusion’s