The probability of conditionals: A review

Reasoning about possibilities: Modal logics, possible worlds, and mental models

Everyone reasons about possibilities. This article explains how they could do so using mental models. The theory makes four major claims: 1. Correct inferences are necessary, referring only to facts or possibilities to which the premises refer and not ruling any of them out, for example: She left or hid; Therefore, it's possible that she left and possible that she hid. 2. A possibility such as that she hid, which is represented in an intuitive model, presupposes the possibility that it did not occur, she did not hide, which, if reasoners deliberate, is represented in the resulting model. 3. Reasoners condense consistent possibilities, such as the earlier pair, into one possibility: it is possible that she left and she hid. 4. Inconsistencies, such as she left or hid, and she neither left nor hid, refer to no possibilities whatsoever - they have an empty model - and so their only effects are local. Hence, any inference can be withdrawn with impunity if there is knowledge to the contrary. Experiments have corroborated each of these principles. They are incompatible with four essentials of standard modal logics, which concern deductions based on "possible" or "necessary". Their formal deductions correspond to valid inferences, which have no counterexamples in which the premises are true but the conclusion is false. And so the article examines the differences between the two approaches, and explores the adaptation of a modal logic to account for correct human reasoning. Its feasibility is an open question.

Human verifications: Computable with truth values outside logic

Cognitive scientists treat verification as a computation in which descriptions that match the relevant situation are true, but otherwise false. The claim is controversial: The logician Gödel and the physicist Penrose have argued that human verifications are not computable. In contrast, the theory of mental models treats verification as computable, but the two truth values of standard logics, true and false, as insufficient. Three online experiments (n = 208) examined participants' verifications of disjunctive assertions about a location of an individual or a journey, such as: 'You arrived at Exeter or Perth'. The results showed that their verifications depended on observation of a match with one of the locations but also on the status of other locations (Experiment 1). Likewise, when they reached one destination and the alternative one was impossible, their use of the truth value: could be true and could be false increased (Experiment 2). And, when they reached one destination and the only alternative one was possible, they used the truth value, true and it couldn't have been false, and when the alternative one was impossible, they used the truth value: true but it could have been false (Experiment 3). These truth values and those for falsity embody counterfactuals. We implemented a computer program that constructs models of disjunctions, represents possible destinations, and verifies the disjunctions using the truth values in our experiments. Whether an awareness of a verification's outcome is computable remains an open question.

A Domain-General Monitoring Account of Bilingual Language Control in Recognition: The Role of Language Dominance and Bilingual Experience

The ability of bilingual individuals to manage two competing languages is assumed to rely on both domain-specific language control and domain-general control mechanisms. However, previous studies have reported mixed findings about the extent and nature of cross-domain generality. The present study examined the role of language dominance, along with bilingual language experience, in the relationship between word recognition and domain-general cognitive control. Two single-language lexical decision tasks (one in L1 and another in L2) and a domain-general flanker task were administered to bilinguals who live in the sociolinguistic context of a minority and a majority language, namely, Uyghur (L1) and Chinese (L2), respectively. The results showed a diversity in language dominance patterns with better performance in L2 than L1 in the recognition modality, even for participants who self-identified as globally being dominant in L1. This finding reflected all bilinguals’ self-evaluation that their preferred language for reading was L2, suggesting that language dominance is dynamic, depending on what language modality is measured. Furthermore, it was found that an earlier onset age of L2 acquisition (but not recent exposure) and a higher across-modality dominance in L2 were related to faster L2 word recognition. When self-reported language dominance was operationalised as a grouping variable, it was further found that both across-modality L1- and L2-dominant bilingual participants demonstrated a significant relationship between L2 word recognition and domain-general monitoring control, while only L1-dominant bilinguals additionally tapped into inhibitory control, indexed by the flanker effect during L2 word recognition. These findings suggest that language dominance has an impact on the extent and nature of the overlap in control mechanisms across specific linguistic and domain-general cognitive domains and add evidence to a domain-general monitoring account of bilingual word recognition.