Conditional reasoning and conditionalization

New normative standards of conditional reasoning and the dual-source model

There has been a major shift in research on human reasoning toward Bayesian and probabilistic approaches, which has been called a new paradigm. The new paradigm sees most everyday and scientific reasoning as taking place in a context of uncertainty, and inference is from uncertain beliefs and not from arbitrary assumptions. In this manuscript we present an empirical test of normative standards in the new paradigm using a novel probabilized conditional reasoning task. Our results indicated that for everyday conditional with at least a weak causal connection between antecedent and consequent only the conditional probability of the consequent given antecedent contributes unique variance to predicting the probability of conditional, but not the probability of the conjunction, nor the probability of the material conditional. Regarding normative accounts of reasoning, we found significant evidence that participants' responses were confidence preserving (i.e., p-valid in the sense of Adams, 1998) for MP inferences, but not for MT inferences. Additionally, only for MP inferences and to a lesser degree for DA inferences did the rate of responses inside the coherence intervals defined by mental probability logic (Pfeifer and Kleiter, 2005, 2010) exceed chance levels. In contrast to the normative accounts, the dual-source model (Klauer et al., 2010) is a descriptive model. It posits that participants integrate their background knowledge (i.e., the type of information primary to the normative approaches) and their subjective probability that a conclusion is seen as warranted based on its logical form. Model fits showed that the dual-source model, which employed participants' responses to a deductive task with abstract contents to estimate the form-based component, provided as good an account of the data as a model that solely used data from the probabilized conditional reasoning task.

A successive-conditionalization approach to disjunctive and syllogistic reasoning

With p and q each standing for a familiar event, a disjunctive statement, "either p or q", seems quite different from its material conditional, "if not p then q". The notions of sufficiency and necessity seem specific to conditional statements. It is surprising, however, to find that perceived sufficiency and necessity affect disjunctive reasoning in the way they affect conditional reasoning. With B and C each standing for a category name, a universal statement, "all B are C", seems stronger than its logically equivalent conditional statement, "if B then C". However, the effects of perceived sufficiency or necessity were found to be as pronounced in conditional reasoning as in syllogistic reasoning. Furthermore, two experiments also showed that (a) MP (modus ponens)-comparable disjunctive reasoning was as difficult as MT (modus tollens)-comparable disjunctive reasoning, and that (b) MT-comparable syllogisms were easier to solve than MT problems in conditional reasoning.

A Mixed Rasch Model of Dual-Process Conditional Reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.

The effect of emotion on interpretation and logic in a conditional reasoning task

The effect of emotional content on logical reasoning is explored in three experiments. Theparticipants completed a conditional reasoning task (If p, then q) with emotional and neutral contents. In Experiment 1, existing emotional and neutral words were used. The emotional value of initially neutral words was experimentally manipulated in Experiments 1B and 2, using classical conditioning. In all experiments, participants were less likely to provide normatively correct answers when reasoning about emotional stimuli, compared with neutral stimuli. This was true for both negative (Experiments 1B and 2) and positive contents (Experiment 2). The participants' interpretations of the conditional statements were also measured (perceived sufficiency, necessity, causality, and plausibility). The results showed the expected relationship between interpretation and reasoning. However, emotion did not affect interpretation. Emotional and neutral conditional statements were interpreted similarly. The results are discussed in light of current models of emotion and reasoning.

Is inferential reasoning just probabilistic reasoning in disguise?

Oaksford, Chater, and Larkin (2000) have suggested that people actually use everyday probabilistic reasoning when making deductive inferences. In two studies, we explicitly compared probabilistic and deductive reasoning with identical if-then conditional premises with concrete content. In the first, adults were given causal premises with one strongly associated antecedent and were asked to make standard deductive inferences or to judge the probabilities of conclusions. In the second, reasoners were given scenarios presenting a causal relation with zero to three potential alternative antecedents. The participants responded to each set of problems under both deductive and probabilistic instructions. The results show that deductive and probabilistic inferences are not isomorphic. Probabilistic inferences can model deductive responses only using a limited, very high threshold model, which is equivalent to a simple retrieval model. These results provide a clearer understanding of the relations between probabilistic and deductive inferences and the limitations of trying to consider these two forms of inference as having a single underlying process.