The conditional in mental probability logic

Pfeifer, Niki; Kleiter, Gernot D.

doi:10.1093/acprof:oso/9780199233298.003.0009

Cited by 66 publications

(105 citation statements)

References 40 publications

Supporting

Mentioning

105

Contrasting

Order By: Relevance

“…Again, the clear majority of participants responded by non-informative intervals, which is predicted by coherence based probability logic. Empirical studies on Gilio's coherence semantics of the basic nonmonotonic reasoning System P [18] provide further empirical support: The clear majority of people infer probabilistically informative and coherent responses in tasks that map the nonmonotonic argument forms of System P [40] but-as predicted-noninformative probabilities in monotonic argument forms [43]. This validates basic rationality norms for nonmonotonic reasoning which govern how conclusions should be retracted in the light of new evidence.…”

Section: Yes Katrin Can Infer Her Certaintymentioning

confidence: 68%

“…Coherence based probability logic also received further strong empirical support by a series of experiments on other examples of the paradoxes of the material conditional: (i) inferring If A, then C from ¬A [44] and (ii) premise strengthening: from If A, then C infer If A ∧ B, then C [43]. Again, the clear majority of participants responded by non-informative intervals, which is predicted by coherence based probability logic.…”

Section: Yes Katrin Can Infer Her Certaintymentioning

confidence: 86%

“…If the tightest coherent probability bounds on the conclusion are constrained by the premises, then the argument is probabilistically informative. If the conclusion probability coincides with the unit interval for all probability assessments of the premises, then the argument is probabilistically non-informative [41].…”

Section: Coherence Based Probability Logicmentioning

confidence: 99%

See 2 more Smart Citations

Reasoning About Uncertain Conditionals

Pfeifer

2013

Stud Logica

Self Cite

View full text Add to dashboard Cite

Abstract.There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants' responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed.I argue why neither logic nor standard probability theory provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view.Keywords: coherence, conditionals, formal epistemology, paradoxes of the material conditional, probability logic, psychology of reasoning Introduction and overviewThere is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. 1 In the psychology of reasoning, the propositional calculus was taken for granted to be the correct normative standard of reference for investigating conditionals [14]. The chosen normative standard of reference guided the construction of psychological theories like a roadmap [37]. Proof-theoretic semantics, for example, stimulated the emergence of two prominent psychological theories of reasoning: Rips' theory of mental rules [47] and Braine and O'Brien's theory of mental logic [6]. Both are rule-based. Likewise, model-theoretic semantics influenced Johnson-Laird's psychological mental models theory [27].Not only psychological theories but also the experimental paradigms for investigating human conditional reasoning were strongly influenced by the Presented by Name of Editor; Received ** **,**** 1 Indicative conditionals are of the form "If A, then C", where the antecedent A and the consequent C are propositions. The ¬A ∧ C and ¬A ∧ ¬C cases are not irrelevant. They rather make A ⊃ C true. Thus, propositional logic also provided rationality criteria for evaluating human inference: Logical validity and the interpretation of indicative conditionals as material conditionals were the most important rationality criteria for assessing human reasoning performance. The participant's interpretation of indicative conditionals was classified as "rational" if, and only if the participant's interpretation is consistent with the semantics of the material conditional. For about ten years now, empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed: More and more psychological studies of reasoning adopted proba...

show abstract

Section: Yes Katrin Can Infer Her Certaintymentioning

confidence: 68%

Section: Yes Katrin Can Infer Her Certaintymentioning

confidence: 86%

See 1 more Smart Citation

Reasoning About Uncertain Conditionals

Pfeifer

2013

Stud Logica

Self Cite

View full text Add to dashboard Cite

show abstract

“…The recent interest in reasoning under uncertainty, more specifically in deductive reasoning with uncertain premises, has led to the elaboration of probabilistic logics (Adams, Uncertain Deduction by Analogy 8 8 1998; Coletti & Scozzafava, 2002;Gilio, 2002;Hailperin, 1996;Pfeifer & Kleiter, 2006, 2009 and their psychological investigation (George, 1995, 1997, Oaksford & Chater, 2007Pfeifer & Kleiter, 2010, 2011Politzer & Bourmaud, 2002). It is to this field of research that we are going to apply the tank analogy.…”

Section: Deduction Under Uncertaintymentioning

confidence: 99%

Deductive Reasoning Under Uncertainty: A Water Tank Analogy

Politzer

2015

Erkenn

View full text Add to dashboard Cite

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.

show abstract

“…Some authors look at the conditional "if A then C", denoted A → C , as the event A c ∨ C (material conditional), but since some years it is becoming standard to look at A → C as the conditional event C|A (see e.g. [4,9]). In [8], based on a complex procedure (which exploits the notion of Stalnaker Bernoulli space), by assuming P (A) positive it is proved that P (A → C) = P (AC) P (A) = P (C|A).…”

Section: Preliminary Notionsmentioning

confidence: 99%

Conjunction, Disjunction and Iterated Conditioning of Conditional Events

Gilio

Sanfilippo

2013

Synergies of Soft Computing and Statistics for Intelligent Data Analysis

View full text Add to dashboard Cite

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold.

show abstract

The conditional in mental probability logic

Cited by 66 publications

References 40 publications

Reasoning About Uncertain Conditionals

Reasoning About Uncertain Conditionals

Deductive Reasoning Under Uncertainty: A Water Tank Analogy

Conjunction, Disjunction and Iterated Conditioning of Conditional Events

Contact Info

Product

Resources

About