Imprecise Uncertain Reasoning: A Distributional Approach (original) (raw)
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8 Uncertain deductive reasoning
The Science of Reason: A Festschrift for …, 2010
Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals).
Towards a mental probability logic
Psychologica Belgica, 2005
We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the "most . . . " quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.
The science of reason: A Festschrift for …, 2011
Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals).
Framing human inference by coherence based probability logic
Journal of Applied Logic, 2009
We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.
Bayesian reasoning with ifs and ands and ors
Frontiers in Psychology, 2015
The Bayesian approach to the psychology of reasoning generalizes binary logic, extending the binary concept of consistency to that of coherence, and allowing the study of deductive reasoning from uncertain premises. Studies in judgment and decision making have found that people's probability judgments can fail to be coherent. We investigated people's coherence further for judgments about conjunctions, disjunctions and conditionals, and asked whether their coherence would increase when they were given the explicit task of drawing inferences. Participants gave confidence judgments about a list of separate statements (the statements group) or the statements grouped as explicit inferences (the inferences group). Their responses were generally coherent at above chance levels for all the inferences investigated, regardless of the presence of an explicit inference task. An exception was that they were incoherent in the context known to cause the conjunction fallacy, and remained so even when they were given an explicit inference. The participants were coherent under the assumption that they interpreted the natural language conditional as it is represented in Bayesian accounts of conditional reasoning, but they were incoherent under the assumption that they interpreted the natural language conditional as the material conditional of elementary binary logic. Our results provide further support for the descriptive adequacy of Bayesian reasoning principles in the study of deduction under uncertainty. Citation: Cruz N, Baratgin J, Oaksford M and Over DE (2015) Bayesian reasoning with ifs and ands and ors. Front. Psychol. 6:192.
Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent
… Symposium on Imprecise Probability: Theories and …, 2007
The modus ponens (A → B, A ∴ B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A → B, ¬A ∴ ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities.
Journal of Pragmatics, 2011
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 affects 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 extensions to probabilistic theories of reasoning to account for the results.
Deductive reasoning from uncertain conditionals
British Journal of Psychology, 2002
This paper begins with a review of the literature on plausible reasoning with deductive arguments containing a conditional premise. There is concurring evidence that people presented with valid conditional arguments such as Modus Ponens and Modus Tollens generally do not endorse the conclusion, but rather find it uncertain, in case (i) the plausibility of the major conditional premise is debatable, (ii) the major conditional premise is formulated in frequentist or probabilistic terms, or (iii) an additional premise introduces uncertainty about the major conditional premise. This third situation gives rise to non monotonic effects by a mechanism that can be characterised as follows: the reasoner is invited to doubt the major conditional premise by doubting the satisfaction of a tacit condition which is necessary for the consequent to occur. Three experiments are presented. The first two aim to generalise the latter result using various types of conditionals and the last shows that performance in conditional reasoning is significantly affected by the representation of the task. This latter point is discussed along with various other issues: we propose a pragmatic account of how the tacit conditions mentioned earlier are treated in plausible reasoning; the relationship of this account with the conditional probability view on conditional sentences is examined; an application of the same account to the Suppression Effect (Byrne, 1989) is proposed and compared with the counterexample availability explanation; and finally some suggestions on how uncertainty could be implemented in a mental logic system are presented.
Journal of Experimental Psychology: Learning, Memory, & Cognition, 2003
- proffered a Bayesian model in which conditional inferences are a direct function of conditional probabilities. In the current article, the authors first considered this model regarding the processing of negatives in conditional reasoning. Its predictions were evaluated against a large-scale meta-analysis (W. J. Schroyens, W. . This evaluation shows that the model is flawed: The relative size of the negative effects does not match predictions. Next, the authors evaluated the model in relation to inferences about affirmative conditionals, again considering the results of a meta-analysis (W. J. Schroyens, W. . The conditional probability model is countered by the data reported in literature; a mental models based model produces a better fit. The authors conclude that a purely probabilistic model is deficient and incomplete and cannot do without algorithmic processing assumptions if it is to advance toward a descriptively adequate psychological theory.