Reasoning From Inconsistency to Consistency.

Abstract

This article presents a theory of how individuals reason from inconsistency to consistency. The theory is based on 3 main principles. First, individuals try to construct a single mental model of a possibility that satisfies a current set of propositions, and if the task is impossible, they infer that the set is inconsistent. Second, when an inconsistency arises from an incontrovertible fact, they retract any singularly dubious proposition or any proposition that is inconsistent with the fact; otherwise, they retract whichever proposition mismatches the fact. A mismatch can arise from a proposition that has only mental models that conflict with the fact or fail to represent it. Third, individuals use their causal knowledge-in the form of models of possibilities-to create explanations of what led to the inconsistency. A computer program implements the theory, and experimental results support each of its principles.

Why some surprises are more surprising than others: Surprise as a metacognitive sense of explanatory difficulty

“…People learn about their environment by explaining it (see Lombrozo, 2012, for a review), whether it be in child development (Piaget, 1952) or education (Adler, 2008), and this explanation process may be triggered by surprise (Ramscar, Dye, Gustafson & Klein, 2013;Tsang, 2013) or inconsistencies (Johnson-Laird, Girotto, & Legrenzi, 2004). These views are echoed in Artificial Intelligence (AI), where surprise has been identified as a cognitive mechanism for identifying learning events in robotic, agent architectures (Bae & Young, 2008Macedo & Cardoso, 2001;Macedo, Reisenzein & Cardoso, 2004;Macedo, Cardoso, Reisenzein, Lorini, & Castelfranchi, 2009).…”

“…They found that the provision of such enabling conditions reduced surprise ratings (see Johnson-Laird et al, 2004, for a discussion of the differences between enabling and causal conditions); but they did not examine explanation productivity or response time. In the context of the present theory, this additional information is seen as providing partial explanations that ease the cognitive load by either (i) directing the retrieval process to more relevant parts of memory, or (ii) directly providing a significant part of the explanation, thus minimising retrieval and inference, or (iii) both (see Figure 3, for a graphical depiction).…”

Against Logical Form

“…Nevertheless, given the putative conclusion that she didn't play a musical instrument, these theories yield its proof from the first and third premises (see, e.g., rips, 1994, p. 116), and there is no obvious way to block the inference. its blocking calls for the detection of the contradiction -no simple matter in formal rule theories (see Johnson-Laird, Girotto, & Legrenzi, 2004) -and some sort of injunction on inferences from contradictions.…”

“…Likewise, the theories have little or nothing to say about how individuals discover that a set of assertions is inconsistent, and what they do to rectify inconsistencies. in contrast, the model theory allows for a process in which they withdraw a conclusion which conflicts with the facts -a form of so-called "nonmonotonic" reasoning (Brewka, Dix, & Konolige, 1997) and then formulate an explanation that resolves the inconsistency (see, e.g., Johnson-Laird, et al, 2004).…”

“…one difficulty with this view, as i mentioned at the outset, is that it offers no obvious explanation of how human beings were able to devise logic and mathematics if they were incapable of deductive reasoning beforehand. Another difficulty is that individuals untrained in logic are able to assess whether or not a set of assertions is consistent (e.g., Johnson-Laird et al, 2004). The task is deductive: a common method in logic to prove that a conclusion follows from premises is to add its negation to the premises, and show that the resulting set of assertions is inconsistent (Jeffrey, 1981).…”