We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a six-sided die, and were asked how sure they were that a conditional holds of the side landing upwards when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto the (...) sides of each die. In two experiments (N1 = 66, N2 = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional’s antecedent and consequent: participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: conditional event interpretations took longer to process than conjunction interpretations (mean difference 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning. (shrink)

According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of events (...) referred to by the antecedent. We manipulated whether the superset was expressed using a disjunction or a hypernym. We also manipulated the source of the dependency, whether in long-term memory or in the stimulus. For subset-consequent conditionals, patterns of responses were mostly conditional probability followed by conjunction. For superset-consequent conditionals, conditional probability responses were most common for hypernym dependencies and least common for disjunction dependencies, which were replaced with responses indicating inferred consequent irrelevance. Conditional probability responses were also more common for knowledge-based than stimulus-based dependencies. We suggest. (shrink)

ABSTRACTTo build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: the conditional event interpretation in the coherencebased probability logic, the discourse processingtheory of Hans Kamp, and the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, (...) a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction. (shrink)

(2013). Statistical models as cognitive models of individual differences in reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 89-102. doi: 10.1080/19462166.2012.674061.

We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(N) essentially arise via congruence relations on classical models of Th(N). We also show that the analogue of Priest's Conjecture for I δ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂ₑ M ⊨ I δ₀ + Exp in any cut [0,a] ⊂e K ⊆ M closed under successor and multiplication.

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.