Byrne has demonstrated that although subjects can make deductively valid inferences of the modus ponens and modus tollens forms, these valid inferences can be suppressed by presenting an appropriate additional premise “If R then Q” with the original conditional “If P then Q”. This suppression effect challenges the assumption of all syntactic theories of conditional reasoning that formal rules of inference such as modus ponens is part of mental logic. This paper argues that both the syntactic and the mental model (...) accounts of the suppression effect are inadequate because they fail to give a principled account of the critical interpretive component involved in reasoning. In contrast, the relative salience model proposed in this study emphasized the centrality of the interpretative processes with the critical component being the relative salience of premises as judged by subjects on the basis of their prior knowledge activated in particular problem situations. Using 120 undergraduates and 120 policemen as subjects, predictions from the model were tested and confirmed in a suppression paradigm and evidence of convergent validity for the construct of salience were obtained. The results cannot be reconciled with either the syntactic view or the mental model view that have dominated theories of conditional reasoning. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

Four experiments are reported which investigated the types of truth tables that people associate with conditional sentences and the kinds of inferences that they will draw from them. The present studies differed from most previous ones in using different types of content in the conditionals, for example promises and warnings. It was found that the type of content had a strong and consistent effect on both truth tables and inferences. It is suggested that this is because in real life conditionals (...) make probabilistic assertions, and that the strength of the probabilistic link is determined by the situation in which the conditional occurs. The implications of these findings for current theories of reasoning are considered and it is concluded that none of them is entirely satisfactory. It is suggested that more linguistically based theories may prove more successful. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Following Marr (1982), any computational account of cognition must satisfy constraints at three explanatory levels: computational, algorithmic, and implementational. This paper focuses on the first two levels and argues that current theories of reasoning cannot provide explanations of everyday defeasible reasoning, at either level. At the algorithmic level, current theories are not computationally tractable: they do not “scale-up” to everyday defeasible inference. In addition, at the computational level, they cannot specify why people behave as they do both on laboratory reasoning (...) tasks and in everyday life (Anderson, 1990). In current theories, logic provides the computational-level theory, where such a theory is evident at all. But logic is not a descriptively adequate computational-level theory for many reasoning tasks. It is argued that better computational-level theories can be developed using a probabilistic framework. This approach is illustrated using Oaksford and Chater's (1994) probabilistic account of Wason's selection task. (shrink)

In certain contexts reasoners reject instances of the valid Modus Ponens and Modus Tollens inference form in conditional arguments. Byrne (1989) observed this suppression effect when a conditional premise is accompanied by a conditional containing an additional requirement. In an earlier study, Rumain, Connell, and Braine (1983) observed suppression of the invalid inferences "the denial of the antecedent" and "the affirmation of the consequent" when a conditional premise is accompanied by a conditional containing an alternative requirement. Here we present three (...) experiments showing that the results of Byrne (1989) and Rumain et al. (1983) are influenced by the answer procedure. When reasoners have to evaluate answer alternatives that only deal with the inferences that can be made with respect to the first conditional, then suppression is observed (Experiment 1). However, when reasoners are also given answer alternatives about the second conditional (Experiment 2) no suppression is observed. Moreover, contrary to the hypothesis of Byrne (1989), at least some of the reasoners do not combine the information of the two conditionals and do not give a conclusion based on the combined premise. Instead, we hypothesise that some of the reasoners have reasoned in two stages. In the first stage, they form a putative conclusion on the basis of the first conditional and the categorical premise, and in the second stage, they amend the putative conclusion in the light of the information in the second premise. This hypothesis was confirmed in Experiment 3. Finally, the results are discussed with respect to the mental model theory and reasoning research in general. (shrink)

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, “if she watered the plants they bloomed,” when beliefs about additional background conditions, for example, “if the sun shone they bloomed” decrease the frequency of inferences such as modus tollens (from “the plants did not bloom” to “therefore she did not water them”). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, “if she had watered the plants they would (...) have bloomed,” when beliefs about the known or presupposed facts, “she did not water the plants and they did not bloom” increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from “she did not water the plants” to “therefore they did not bloom”) is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new “switched‐suppression” effect for conditionals with negated components, for example, “if she had not watered the plants they would not have bloomed”: modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning. (shrink)

How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly (...) stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)

The suppression of the Modus Ponens inference is described as a loss of confidence in the conclusion C of an argument ''If A1 then C; If A2 then C; A1'' where A2 is a requirement for C to happen. It is hypothesised that this loss of confidence is due to the derivation of the conversational implicature ''there is a chance that A2 might not be satisfied'', and that different syntactic introductions of the requirement A2 (e.g., ''If C then A2'') will (...) lead to various frequencies in the derivation of this implicature, according to previous studies in the field of causal explanation. An experiment is conducted, whose results support those claims. Results are discussed in the light of the Mental Logic and Mental Model theories, as well as in the light of the pragmatic approach to uncertain reasoning. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the psychology (...) of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)