Does the inclusive disjunction really mean the conjunction of possibilities?

Wang, Moyun; Zheng, Liyuan

doi:10.1016/j.cognition.2020.104551

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…Thus, the conjunction of possibilities postulated by MMT2 is untenable. This is consistent with the previous finding that people tend to interpret a singular disjunction as the disjunction of possibilities allowed by it (Wang & Zheng, 2021).…”

Section: Discussionsupporting

confidence: 93%

A rule violation account for the reading of negated general disjunctions

Wang¹

2021

Preprint

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Few previous studies have investigated how people read the negation of a general disjunction that refers to a set of objects (It is not true that xs are p or q). We develop four alternative accounts for the negation. The original mental model theory interprets the negation as the negation of the disjunction of possibilities allowed by the general disjunction. The revised mental model theory interprets it as the negation of the conjunction of possibilities allowed by the general disjunction. The probabilistic violation account interprets it as the probabilistic violation of the general disjunction by introducing nonnegligible exceptions. A normative semantic violation account interprets the negation as the semantic qualitative violation of the general disjunction by introducing exceptions. Three experiments systematically investigated the reading of negated general disjunctions in different possibility and truth judgment tasks. Participants’ possibility and truth judgments provide convergent evidence that a negated general disjunction is consistent with only sets containing ¬p¬q cases regardless of whether other cases are present or not, and people prefer to the semantic violation interpretation of negated general disjunctions. These findings favour the semantic violation account over the other accounts. This implies that the core meaning of a general disjunction is the rule represented by it, but not the set of possibilities referred to by it.

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Section: Discussionsupporting

confidence: 93%

A rule violation account for the reading of negated general disjunctions

Wang¹

2021

Preprint

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“…In the PP response pattern of ¬pq / ¬p¬q, the category inference that the corresponding set possibly includes ¬pq / ¬p¬q cases implies that it possibly excludes or excludes ¬pq / ¬p¬q cases, and ¬pq / ¬p¬q may be possible or impossible for the instance and is irrelevant to the conditional, and so the ¬pq / ¬p¬q possibility is unrequired by the true conditional. Thus, the instance inference that participants judged ¬pq / ¬p¬q possible for the instance may be due to the heuristic that in abstract contexts no available evidence can rule out the ¬pq / ¬p¬q possibility, as is suggested by Oaksford, Over, & Cruz (2019) and Wang & Zheng (2021). Overall, the difference between the above two response patterns implies that for a true conditional, the pq possibility is required and relevant, but the ¬pq / ¬p¬q possibility is not.…”

Section: Resultsmentioning

confidence: 87%

Consistency and inconsistency between instance and categorical modal inferences from conditionals

Wang¹

2021

Preprint

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For the modal meanings of conditionals with the form if p then q, there are three existing psychological accounts: the original suppositional theory, the original and revised mental models theory. They imply different modal meanings of if p then q. Alternatively, we propose a revised suppositional theory with the unique prediction that the set from which the instance referred to by a true conditional was randomly drawn, necessarily includes pq cases, and possibly includes ¬pq / ¬p¬q cases, but impossibly includes p¬q cases. One experiment investigated whether category modal inferences from a conditional would be consistent with preceding instance modal inferences from it. The results revealed that (1) previous instance inferences did not affect subsequent category inferences; (2) relevant cases pq and p¬q tended to elicit consistent response patterns, but irrelevant cases ¬pq and ¬p¬q tended to elicit inconsistent response patterns; (3) the overall response pattern of category inferences is consistent with only the prediction of the revised suppositional theory. The latter implies that only the pq possibility is required by a true conditional, but the ¬pq / ¬p¬q possibility is unrequired. On the whole, these findings favor the revised suppositional theory over the other accounts.

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“…In fact, Wang and Zheng (2021) found that people interpret an inclusive disjunction, p or q , as the extensional disjunction, pq or p¬q or ¬pq , as found in MMT1, but not as the modal conjunction, possible pq & possible p¬q & possible ¬pq , as newly proposed in MMT2. In the present research, we have found evidence against the MMT2 representation of a conditional if p then q as the modal conjunction possible pq & possible ¬pq & possible ¬p¬q .…”

Section: Discussionmentioning

confidence: 88%

Section: Discussionmentioning

confidence: 99%

“…The present study on the interpretation of conditionals is an extension of Wang and Zheng (2021) on the interpretation of disjunctions. All these studies are novel in critically examining the new modal approach of MMT2, which Khemlani et al (2018) described in the following (with our additions in brackets):“The previous version [MMT1] of the model theory postulated that people understand compound assertions by constructing models representing the disjunctive alternatives to which they refer.…”

Section: Discussionmentioning

confidence: 99%

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What is required for the truth of a general conditional?

Wang

Over

Liang

2022

Quarterly Journal of Experimental Psychology

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General conditionals, if p then q, can be used to make assertions about sets of objects. Previous studies have found that people generally judge the probability of one these conditionals to be the conditional probability of q given p, P(q|p). Two experiments investigated the qualitative relation between the exhaustive possibilities, p & q, p & ¬q, ¬p & q, and ¬p & ¬q, and truth and possibility judgments about general conditionals. In Experiment 1, for truth judgments, people evaluated a general conditional as "true" in sets containing p & q cases but no p & ¬q, and "true" judgments depended only on P(q|p). In Experiment 2, for possibility judgments, people's responses implied that only p & q cases have to be possible in a set for a general conditional to be true of the set. Our results add to earlier findings against representing a general conditional as the material conditional of extensional logic, and they provide novel disconfirmation of two recent proposals: the modal semantics of revised mental model theory and certain inferentialist accounts of conditionals. They supply new support for suppositional theories of conditionals.

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Does the inclusive disjunction really mean the conjunction of possibilities?

Cited by 4 publications

References 7 publications

A rule violation account for the reading of negated general disjunctions

A rule violation account for the reading of negated general disjunctions

Consistency and inconsistency between instance and categorical modal inferences from conditionals

What is required for the truth of a general conditional?

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