Reasoning About Uncertain Conditionals (original) (raw)
Related papers
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.
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.
A process model of the understanding of uncertain conditionals
Thinking & Reasoning
To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) 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.
Conditional Probability and the Cognitive Science of Conditional Reasoning
Mind and Language, 2003
This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context.
Uncertain conditionals and counterfactuals in (non-)causal settings
Conditionals are basic for human reasoning. In our paper, we present two experiments, which for the first time systematically compare how people reason about indicative conditionals (Experiment 1) and counterfactual conditionals (Experiment 2) in causal and non-causal task settings (N = 80). The main result of both experiments is that conditional probability is the dominant response pattern and thus a key ingredient for modeling causal, indicative, and counterfactual conditionals. In the paper, we will give an overview of the main experimental results and discuss their relevance for understanding how people reason about conditionals.
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).
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).
Is Human Reasoning about Nonmonotonic Conditionals Probabilistically Coherent?
Nonmonotonic conditionals (A js B) are formalizations of common sense expressions of the form \if A, normally B". The nonmonotonic conditional is interpreted by a \high" coherent conditional probability, P (BjA) > :5. Two important properties are closely related to the non- monotonic conditional: First, A js B allows for exceptions. Second, the rules of the nonmonotonic system p guiding A js B allow for withdrawing conclusions in the light of new premises. This study reports a series of three experiments on reasoning with inference rules about nonmonotonic conditionals in the framework of co- herence. We investigated the cut, and the right weakening rule of sys- tem p. As a critical condition, we investigated basic monotonic properties of classical (monotone) logic, namely monotonicity, transitivity, and contraposition. The results suggest that people reason nonmonotoni- cally rather than monotonically. We propose nonmonotonic reasoning as a competence model of human re...
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.