Probabilities, causation, and logic programming in conditional reasoning: reply to Stenning and Van Lambalgen (2016)

ABSTRACT

Oaksford and Chater (2014, Thinking and Reasoning, 20, 269–295) critiqued the logic programming (LP) approach to nonmonotonicity and proposed that a Bayesian probabilistic approach to conditional reasoning provided a more empirically adequate theory. The current paper is a reply to Stenning and van Lambalgen's rejoinder to this earlier paper entitled ‘Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater’ (2016) in Thinking and Reasoning. It is argued that causation is basic in human cognition and that explaining how abnormality lists are created in LP requires causal models. Each specific rejoinder to the original critique is then addressed. While many areas of agreement are identified, with respect to the key differences, it is concluded the current evidence favours the Bayesian approach, at least for the moment.

KEYWORDS:

• Probability
• causation
• logical programming
• causal Bayes nets

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ As Cartwright (1983) observes, any probabilistic analysis ends up having to define a probabilistic relation that keeps all other causally relevant factors constant, i.e., it is circular as a definition. As Stalnaker (1984) observes, degrees of similarity and difference between possible worlds depend on similarities with respect to causal properties, and so again circularity beckons.

² We do not understand the purpose of the reference to “buying contact lenses” in the description of the MP-neutral condition.

³ Although this is an actual example of the materials used in Pijnacker et al. (2010), which may lead to questions over their results. However, unlike this example, Pijnacker et al. (2010) used a neutral context sentence in place of L.

⁴ Van Lambalgen and Hamm (2004) is a book implementing the event calculus in LP. It is a logico-linguistic work, which few psychologists of reasoning behaviour are likely to have read, bar S and L.

⁵ As we observed, only the German suffix “ver” seemed to be a possible candidate. The old adage, “the exception proves the rule” also comes close. However, if you are like us, then when you first encountered this adage, it sounded paradoxical.

⁶ Of course, this is hardly a novel proposal (e.g., Johnson-Laird, 1983), although there is now active debate about the nature of these small-scale models of the world which people construct in order to draw inferences.

⁷ Localist NNs should not be conflated with local inference. Localist NNs assume non-distributed representations of object and events, e.g., there is one unit to represent, say cat.

⁸ We also agree with SL that a lot of the action is at the System 1/model interface and that System 2, involving language and handling alternatives, remains very underspecified in dual-systems approaches.

⁹ This comment was rather obscure and we would value seeing it elaborated.

¹⁰ In the noisy–OR rule, the strength of a dependency is treated as inversely proportional to the number of disablers, which is partially consistent with the approach SL discuss later. However, in the noisy–OR representation, a disabler's disabling strength is also taken in to account, which SL's approach cannot deal with.

¹¹ In the similar factorial designs used by Cummins (1995), effect sizes were not reported, so we cannot determine whether in these studies, number of different disablers “...explains[s] a good deal of variance..” or not. In Geiger and Oberauer (2007), it was the lack of any such effect that was the upshot of the paper.

¹² In LP, we assume “consistency” is not classical consistency (for any proposition p, p and ¬p is not derivable) but some three-valued alternative—the underlying logic is apparently Kleene's strong three-valued system (Haack, 1974).

¹³ We say “potentially” because the proposal and its consequences remain to be full worked through.

¹⁴ We spare the reader a very long list of citations establishing this claim but rather refer the reader to the most recent textbook on thinking and reasoning (Manktelow, 2012) where the new paradigm features heavily.