The Psychological Reality of Classical Quantifier Entailment Properties

A test of directional entailment properties of classical quantifiers defined by the theory of generalised quantifiers (Barwise and Cooper, 1981) is described. Participants had to solve a task which consisted of four kinds of inference. In the first one, the premise was of the type Q - hyponym - verb - blank predicate, where Q is a classical quantifier, (e. g., some cats are [ ] ), and the question was to indicate what, if anything, can be concluded by filling up the slots in ........- hyperonym - verb - blank predicate (e. g., ........animals are [ ] ). The second kind of inference was the same, except that the hyperonym was in the premise and the hyponym in the conclusion. The third and fourth kinds of inference differed from the first two by the position of the hyperonym (resp. hyponym) which occupied the place of the predicate (e. g., some [ ] are animals). It was observed that when the directional entailment holds people respond accorddingly in most cases and that when the entailment does not hold they correctly fail to produce it. These results provide elementary, but essential empirical support to this semantic approach to quantification, as well as a prerequisite for its application to the study of reasoning with quantifiers. The implications for the psychology of reasoning are discussed

premise interpretation in conditional reasoning

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Solving natural syllogisms

Natural syllogisms are expressed in terms of classes and properties of the real world (usually of daily life). They exploit a categorisation present in semantic memory that provides a class inclusion structure. they are enthymematic (the class inclusion of the minor premise is implicit) and typically occur within a dialogue. Their form is identical to a formal syllogism once the minor premise is made explicit. It is claimed that reasoners routinely execute natural_syllogisms in an effortless manner based on ecthesis, which is primed by the class inclusion structure kept in long term memory

Reasoning, judgment and pragmatics

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Could it be the case that if I am right my opponents will be pleased? A rejoinder to Johnson-Laird, Byrne and Girotto

I take up the four issues considered by Johnson-Laird, Byrne and Girotto in their reply to Politzer (2007). Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one (truth functionality) and can be attenuated about the second one (the paradoxes of material implication). However, I maintain and refine my criticisms on the last two (negation and the probability of conditionals), backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals

Deductive Reasoning Under Uncertainty Using a Water Tank Analogy

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds would commit themselves to executing physically impossible tasks

Reasoning with conditionals

This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second part, the main theories of deductive reasoning (mental rules, mental models, and the probabilistic approach) are considered in turn; their content is summarised and the semantics they assume for if and the way they explain formal conditional reasoning are discussed, in particular in the light of experimental work on the probability of conditionals. The last part presents the recent shift of interest towards the study of conditional reasoning in context, that is, with large knowledge bases and uncertain premises

Solving categorical syllogisms with singular premises

We elaborate on the approach to syllogistic reasoning based on "case identification" (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition (ecthesis), and that there are traces of this method in the strategies described by a number of psychologists, from Störring (1908) to the present day. It was hypothesised that by rendering individual cases explicit in the premises the chance that reasoners engage in a proof by exposition would be enhanced, and thus performance improved. To do so, we used syllogisms with singular premises (e. g., this X is Y). This resulted in a uniform increase in performance as compared to performance on the associated standard syllogisms. These results cannot be explained by the main theories of syllogistic reasoning in their current state