Logic, probability, and human reasoning

How people think about the truth of hypothetical impossibilities

People can think about hypothetical impossibilities and a curious observation is that some impossible conditionals seem true and others do not. Four experiments test the proposal that people think about impossibilities just as they do possibilities, by attempting to construct a consistent simulation of the impossible conjecture with its suggested outcome, informed by their knowledge of the real world. The results show that participants judge some impossible conditionals true with one outcome, for example, "if people were made of steel, they would not bruise easily" and false with the opposite outcome, "if people were made of steel they would bruise easily", and others false with either outcome, for example, "if houses were made of spaghetti, their engines would (not) be noisy". However, they can sometimes judge impossible conditionals true with either outcome, for example, "if Plato were identical to Socrates, he would (not) have a small nose", or "if sheep and wolves were alike, they would (not) eat grass". The results were observed for judgments about what could be true (Experiments 1 and 4), judgments of degrees of truth (Experiment 2), and judgments of what is true (Experiment 3). The results rule out the idea that people evaluate the truth of a hypothetical impossibility by relying on cognitive processes that compare the probability of each conditional to its counterpart with the opposite outcome.

The reemergence of the language-of-thought hypothesis: Consequences for the development of the logic of thought

Quilty-Dunn et al. defended the reemergence of language-of-thought hypothesis (LoTH). My commentary builds up implications for the study of the development of our logical capacities. Empirical support for logically augmented LoT systems calls for the investigation of their logical primitives and developmental origin. Furthermore, Quilty-Dunn et al.'s characterization of LoT helps the quest for the foundation of logic by dissociating logical cognition from natural language.

Modelling Differential Diagnosis of Febrile Diseases with Fuzzy Cognitive Map

The report of the World Health Organization (WHO) about the poor accessibility of people living in low-to-middle-income countries to medical facilities and personnel has been a concern to both professionals and nonprofessionals in healthcare. This poor accessibility has led to high morbidity and mortality rates in tropical regions, especially when such a disease presents itself with confusable symptoms that are not easily differentiable by inexperienced doctors, such as those found in febrile diseases. This prompted the development of the fuzzy cognitive map (FCM) model to serve as a decision-support tool for medical health workers in the diagnosis of febrile diseases. With 2465 datasets gathered from four states in the febrile diseases-prone regions in Nigeria with the aid of 60 medical doctors, 10 of those doctors helped in weighting and fuzzifying the symptoms, which were used to generate the FCM model. Results obtained from computations to predict diagnosis results for the 2465 patients, and those diagnosed by the physicians on the field, showed an average of 87% accuracy for the 11 febrile diseases used in the study. The number of comorbidities of diseases with varying degrees of severity for most patients in the study also covary strongly with those found by the physicians in the field.

Probabilistic and Deductive Reasoning in the Human Brain

Reasoning is a process of inference from given premises to new conclusions. Deductive reasoning is truth-preserving and conclusions can only be either true or false. Probabilistic reasoning is based on degrees of belief and conclusions can be more or less likely. While deductive reasoning requires people to focus on the logical structure of the inference and ignore its content, probabilistic reasoning requires the retrieval of prior knowledge from memory. Recently, however, some researchers have denied that deductive reasoning is a faculty of the human mind. What looks like deductive inference might actually also be probabilistic inference, only with extreme probabilities. We tested this assumption in an fMRI experiment with two groups of participants: one group was instructed to reason deductively, the other received probabilistic instructions. They could freely choose between a binary and a graded response to each problem. The conditional probability and the logical validity of the inferences were systematically varied. Results show that prior knowledge was only used in the probabilistic reasoning group. These participants gave graded responses more often than those in the deductive reasoning group and their reasoning was accompanied by activations in the hippocampus. Participants in the deductive group mostly gave binary responses and their reasoning was accompanied by activations in the anterior cingulate cortex, inferior frontal cortex, and parietal regions. These findings show that (1) deductive and probabilistic reasoning rely on different neurocognitive processes, (2) people can suppress their prior knowledge to reason deductively, and (3) not all inferences can be reduced to probabilistic reasoning.

Coherence, not conditional meaning, accounts for the relevance effect

Missing-link conditionals like "If bats have wings, Paris is in France" are generally felt to be unacceptable even though both clauses are true. According to the Hypothetical Inferential Theory, this is explained by a conventional requirement of an inferential connection between conditional clauses. Bayesian theorists have denied the need for such a requirement, appealing instead to a requirement of discourse coherence that extends to all ways of connecting clauses. Our experiment compared conditionals ("If A, C"), conjunctions ("A and C"), and bare juxtapositions ("A. C."). With one systematic exception that is predicted by prior work in coherence theory, the presence or absence of an inferential link affected conditionals and other statement types in the same way. This is as expected according to the Bayesian approach together with a general theory of discourse coherence.

Reasoning About Want

No present theory explains the inferences people draw about the real world when reasoning about "bouletic" relations, that is, predicates that express desires, such as want in "Lee wants to be in love". Linguistic accounts of want define it in terms of a relation to a desirer's beliefs, and how its complement is deemed desirable. In contrast, we describe a new model-based theory that posits that by default, desire predicates such as want contrast desires against facts. In particular, A wants P implies by default that P is not the case, because you cannot want what is already true. On further deliberation, reasoners may infer that A believes, but does not know for certain, that P is not the case. The theory makes several empirical predictions about how people interpret, assess the consistency of, and draw conclusions from desire predicates like want. Seven experiments tested and validated the theory's central predictions. We assess the theory in light of recent proposals of desire predicates.

EXPRESS: What is required for the truth of a general conditional?

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.

Logic, Probability, and Pragmatics in Syllogistic Reasoning

Syllogistic reasoning lies at the intriguing intersection of natural and formal reasoning of language and logic. Syllogisms comprise a formal system of reasoning yet make use of natural language quantifiers (e.g., all, some) and invite natural language conclusions. The conclusions people tend to draw from syllogisms, however, deviate substantially from the purely logical system. Are principles of natural language understanding to blame? We introduce a probabilistic pragmatic perspective on syllogistic reasoning: We decompose reasoning with natural language arguments into two subproblems: language comprehension and language production. We formalize models of these processes within the Rational Speech Act framework and explore the pressures that pragmatic reasoning places on the production of conclusions. We test our models on a recent, large data set of syllogistic reasoning and find that the selection process of conclusions from syllogisms are best modeled as a pragmatic speaker who has the goal of aligning the beliefs of a naive listener with those of their own. We compare our model to previously published models that implement two alternative theories-Mental Models and Probability Heuristics-finding that our model quantitatively predicts the full distributions of responses as well as or better than previous accounts, but with far fewer parameters. Our results suggest that human syllogistic reasoning may be best understood not as a poor approximation to ideal logical reasoning, but rather as rational probabilistic inference in support of natural communication.

A Revised Framework for the Investigation of Expectation Update Versus Maintenance in the Context of Expectation Violations: The ViolEx 2.0 Model

Expectations are probabilistic beliefs about the future that shape and influence our perception, affect, cognition, and behavior in many contexts. This makes expectations a highly relevant concept across basic and applied psychological disciplines. When expectations are confirmed or violated, individuals can respond by either updating or maintaining their prior expectations in light of the new evidence. Moreover, proactive and reactive behavior can change the probability with which individuals encounter expectation confirmations or violations. The investigation of predictors and mechanisms underlying expectation update and maintenance has been approached from many research perspectives. However, in many instances there has been little exchange between different research fields. To further advance research on expectations and expectation violations, collaborative efforts across different disciplines in psychology, cognitive (neuro)science, and other life sciences are warranted. For fostering and facilitating such efforts, we introduce the ViolEx 2.0 model, a revised framework for interdisciplinary research on cognitive and behavioral mechanisms of expectation update and maintenance in the context of expectation violations. To support different goals and stages in interdisciplinary exchange, the ViolEx 2.0 model features three model levels with varying degrees of specificity in order to address questions about the research synopsis, central concepts, or functional processes and relationships, respectively. The framework can be applied to different research fields and has high potential for guiding collaborative research efforts in expectation research.

The Brain Structure and Intrinsic Characters of Falsification Thinking in Conditional Proposition Testing

Wason's selection task (WST) as a representative of the field of conditional proposition testing has been explored by multiple disciplines for more than 50 years, but the neural basis of its key falsification thinking remains unclear. Considering that the accuracy of individuals in WST has stability over time, we believe that falsification thinking has a specific brain structural basis and intrinsic neural characteristics. To test this hypothesis, we studied individuals who were able to complete the WST using T1-weighted MRI (using voxel-based morphology (VBM) analysis) and resting electroencephalogram (EEG) (using microstate analysis, which can reflect stable cognitive characteristics of individuals) techniques. First, VBM analysis found that, compared with the verification group, the gray matter volume (GMV) of the left inferior temporal gyrus and the right superior temporal region of the falsification group was larger, whereas the GMV in the cerebellum of the verification group was significantly larger than that of the falsification group. Subsequently, the results of the microstate analysis of the resting EEG data showed that the contribution of class A of the falsification group, which is closely related to the language network, is significantly higher than that of the verification group. Our structural MRI and resting EEG results consistently show that the structure and intrinsic activity pattern of the temporal lobe in individuals with falsification thinking are specific. Furthermore, the findings may provide potential insights into the role of the temporal lobe (which is also a brain region of language processing) in thought.

Which cognitive individual differences predict good Bayesian reasoning? Concurrent comparisons of underlying abilities

We know a lot about how to present Bayesian reasoning tasks in order to aid performance, but less about underlying individual differences that can account for interindividual variability on the same tasks. Such information would be useful for both theoretical and practical reasons. Two theoretical positions, ecological rationality and nested set views, generate multiple hypotheses about which individual difference traits should be most relevant as underlying Bayesian reasoning performance. However, because many of these traits are somewhat overlapping, testing variables in isolation can yield misleading results. The present research assesses Bayesian reasoning abilities in conjunction with multiple individual different measures. Across three experiments, Bayesian reasoning was best predicted by measures of numerical literacy and visuospatial ability, as opposed to several different measures of cognitive thinking dispositions/styles, ability to conceptually model set-theoretic relationships, or cognitive processing ability (working memory span). These results support an ecological rationality view of Bayesian reasoning, rather than nested sets views. There also was some predictive ability for the Cognitive Reflection Task, which was only partially due to the numeracy aspects of that instrument, and further work is needed to clarify if this is a distinct factor. We are now beginning to understand not only how to build Bayesian reasoning tasks, but also how to build good Bayesian reasoners.

Can conditionals explain explanations? A modus ponens model of B because A

We suggest a normative model for the evaluation of explanations B because A based on probabilistic conditional reasoning and compare it with empirical data. According to the modus ponens model of explanations, the probability of B because A should equal the joint probability of the conditional if A then B and the explanans A. We argue that B because A expresses the conjunction of A and B as well as positive relevance of A for B. In Study 1, participants (N = 80) judged the subjective probabilities of 20 sets of statements with a focus on belief-based reasoning under uncertainty. In Study 2, participants (N = 376) were assigned to one of six item sets for which we varied the inferential relevance of A for B to explore boundary conditions of our model. We assessed the performance of our model across a range of analyses and report results on the Equation, a fundamental model in research on probabilistic reasoning concerning the evaluation of conditionals. In both studies, results indicate that participants' belief in statements B because A followed model predictions systematically. However, a sizeable proportion of sets of beliefs contained at least one incoherence, indicating deviations from the norms of rationality suggested by our model. In addition, results of Study 2 lend support to the idea that inferential relevance may be relevant for the evaluation of both conditionals and explanations.

The probability of conditionals: A review

A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory.

Causal judgments about atypical actions are influenced by agents' epistemic states

A prominent finding in causal cognition research is people's tendency to attribute increased causality to atypical actions. If two agents jointly cause an outcome (conjunctive causation), but differ in how frequently they have performed the causal action before, people judge the atypically acting agent to have caused the outcome to a greater extent. In this paper, we argue that it is the epistemic state of an abnormally acting agent, rather than the abnormality of their action, that is driving people's causal judgments. Given the predictability of the normally acting agent's behaviour, the abnormal agent is in a better position to foresee the consequences of their action. We put this hypothesis to test in four experiments. In Experiment 1, we show that people judge the atypical agent as more causal than the normally acting agent, but also judge the atypical agent to have an epistemic advantage. In Experiment 2, we find that people do not judge a causal difference if no epistemic advantage for the abnormal agent arises. In Experiment 3, we replicate these findings in a scenario in which the abnormal agent's epistemic advantage generalises to a novel context. In Experiment 4, we extend these findings to mental states more broadly construed and develop a Bayesian network model that predicts the degree of outcome-oriented mental states based on action normality and epistemic states. We find that people infer mental states like desire and intention to a greater extent from abnormal behaviour when this behaviour is accompanied by an epistemic advantage. We discuss these results in light of current theories and research on people's preference for abnormal causes.

Age-related differences in structural and functional prefrontal networks during a logical reasoning task

In logical reasoning, difficulties in inhibition of currently-held beliefs may lead to unwarranted conclusions, known as belief bias. Aging is associated with difficulties in inhibitory control, which may lead to deficits in inhibition of currently-held beliefs. No study to date, however, has investigated the underlying neural substrates of age-related differences in logical reasoning and the impact of belief load. The aim of the present study was to delineate age differences in brain activity during a syllogistic logical reasoning task while the believability load of logical inferences was manipulated. Twenty-nine, healthy, younger and thirty, healthy, older adults (males and females) completed a functional magnetic resonance imaging experiment in which they were asked to determine the logical validity of conclusions. Unlike younger adults, older adults engaged a large-scale network including anterior cingulate cortex and inferior frontal gyrus during conclusion stage. Our functional connectivity results suggest that while older adults engaged the anterior cingulate network to overcome their intuitive responses for believable inferences, the inferior frontal gyrus network contributed to higher control over responses during both believable and unbelievable conditions. Our functional results were further supported by structure-function-behavior analyses indicating the importance of cingulum bundle and uncinate fasciculus integrity in rejection of believable statements. These novel findings lend evidence for age-related differences in belief bias, with potentially important implications for decision making where currently-held beliefs and given assumptions are in conflict.

Much Ado About Nothing: The Mental Representation of Omissive Relations

When the absence of an event causes some outcome, it is an instance of omissive causation. For instance, not eating lunch may cause you to be hungry. Recent psychological proposals concur that the mind represents causal relations, including omissive causal relations, through mental simulation, but they disagree on the form of that simulation. One theory states that people represent omissive causes as force vectors; another states that omissions are representations of contrasting counterfactual simulations; a third argues that people think about omissions by representing sets of iconic possibilities – mental models – in a piecemeal fashion. In this paper, we tease apart the empirical predictions of the three theories and describe experiments that run counter to two of them. Experiments 1 and 2 show that reasoners can infer temporal relations from omissive causes – a pattern that contravenes the force theory. Experiment 3 asked participants to list the possibilities consistent with an omissive cause – it found that they tended to list particular privileged possibilities first, most often, and faster than alternative possibilities. The pattern is consistent with the model theory, but inconsistent with the contrast hypothesis. We marshal the evidence and explain why it helps to solve a long-standing debate about how the mind represents omissions.

Does the inclusive disjunction really mean the conjunction of possibilities?

There is an ongoing dispute in the psychology of reasoning about how people interpret disjunctions, p or q. In the original mental models theory (MMT1) people interpret p or q as the disjunction of three possibilities (possibly p¬q, or possibly ¬pq, or possibly pq, where "¬" = not). p or q is true if one disjunct is actually true. In a recent revision of mental models theory (MMT2), people interpret p or q as a conjunction of the three possibilities, and they treat it as true only if each is possible and ¬p¬q is impossible. Two experiments investigated possibility and truth judgments about disjunctions given sets consisting of one or more of the four cases (p¬q, ¬pq, pq, and ¬p¬q). The results showed that in both possibility and truth judgments, participants' interpretations of disjunctions were only consistent with MMT1. Inclusive disjunctions imply the disjunction of the three possibilities, and they are true when one of the three cases (p¬q, ¬pq, and pq) is actual. These findings support MMT1, but not MMT2. In conclusion, the revised mental models theory may be unnecessary for disjunctions.

Reasoning about Durations

A set of assertions is consistent provided they can all be true at the same time. Naive individuals could prove consistency using the formal rules of a logical calculus, but it calls for them to fail to prove the negation of one assertion from the remainder in the set. An alternative procedure is for them to use an intuitive system (System 1) to construct a mental model of all the assertions. The task should be easy in this case. However, some sets of consistent assertions have no intuitive models and call for a deliberative system (System 2) to construct an alternative model. Formal rules and mental models therefore make different predictions. We report three experiments that tested their respective merits. The participants assessed the consistency of temporal descriptions based on statements using "during" and "before." They were more accurate for consistent problems with intuitive models than for those that called for deliberative models. There was no robust difference in accuracy between consistent and inconsistent problems. The results therefore corroborated the model theory.

Conditionals and testimony

Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much-perhaps most-of what we believe through the testimony of others, the simple matter of acquiring conditionals via others' assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning - a challenge which no account presently fully meets.

Reasoning about epistemic possibilities

Reasoning about epistemic possibilities - those based on knowledge - is fundamental in daily life. It is formalized in modal logics, of which there are infinitely many, based on the semantics of 'possible worlds'. An alternative psychological theory postulates that possibilities (and probabilities) in daily life are based on the human ability to construct mental models of finite alternatives, which can each be realized in an indefinite number of different ways. This account leads to three main predictions that diverge from normal modal logics. First, the assertion of an epistemic possibility, A, presupposes the possibility of not-A, in default of knowledge to the contrary. Second, reasoners condense multiple possibilities into one, contravening modal logics, but reducing the load on working memory, e.g.: When knowledge shows that this condensation would be inconsistent, reasoners resist it. Epistemic possibilities are akin to non-numerical probabilities, forming a scale that runs from impossible to certain. In contrast, epistemic necessities state a necessary condition for some other proposition, e.g.: "It is necessary that it rains tomorrow for the plants to survive." The article reports five experiments corroborating these predictions. Their results challenge current conceptions of human reasoning.

Risk communication in cyberspace: a brief review of the information-processing and mental models approaches

Effective risk communication in cyberspace is critical for users to understand the potential security risks and make secure decisions. Two approaches to risk communication originating from psychology, the human information-processing approach and the mental-models approach, have been widely applied in other research fields of risk communication. The human information-processing approach characterizes the human as a communication system, with risk-communication information from a source delivered to the receiver, who processes the information via various stages. The mental-models approach emphasizes the importance of understanding experts' and non-experts' mental models, comparing these models, and drafting and evaluating risk-communication messages. With an overview of these two approaches and their applications, the goal of this paper is to provide insights for future use of these approaches in cybersecurity.

Possibilities and the parallel meanings of factual and counterfactual conditionals

The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

A Process Model of Causal Reasoning

How do we make causal judgments? Many studies have demonstrated that people are capable causal reasoners, achieving success on tasks from reasoning to categorization to interventions. However, less is known about the mental processes used to achieve such sophisticated judgments. We propose a new process model-the mutation sampler-that models causal judgments as based on a sample of possible states of the causal system generated using the Metropolis-Hastings sampling algorithm. Across a diverse array of tasks and conditions encompassing over 1,700 participants, we found that our model provided a consistently closer fit to participant judgments than standard causal graphical models. In particular, we found that the biases introduced by mutation sampling accounted for people's consistent, predictable errors that the normative model by definition could not. Moreover, using a novel experimental methodology, we found that those biases appeared in the samples that participants explicitly judged to be representative of a causal system. We conclude by advocating sampling methods as plausible process-level accounts of the computations specified by the causal graphical model framework and highlight opportunities for future research to identify not just what reasoners compute when drawing causal inferences, but also how they compute it.

Role of the Hippocampus During Logical Reasoning and Belief Bias in Aging

Reasoning requires initial encoding of the semantic association between premises or assumptions, retrieval of these semantic associations from memory, and recombination of information to draw a logical conclusion. Currently-held beliefs can interfere with the content of the assumptions if not congruent and inhibited. This study aimed to investigate the role of the hippocampus and hippocampal networks during logical reasoning tasks in which the congruence between currently-held beliefs and assumptions varies. Participants of younger and older age completed a series of syllogistic reasoning tasks in which two premises and one conclusion were presented and they were required to decide if the conclusion logically followed the premises. The belief load of premises was manipulated to be either congruent or incongruent with currently-held beliefs. Our whole-brain results showed that older adults recruited the hippocampus during the premise integration stage more than their younger counterparts. Functional connectivity using a hippocampal seed revealed that older, but not younger, adults recruited a hippocampal network that included anterior cingulate and inferior frontal regions when premises were believable. Importantly, this network contributed to better performance in believable inferences, only in older adults group. Further analyses suggested that, in older adults group, the integrity of the left cingulum bundle was associated with the higher rejection of believable premises more than unbelievable ones. Using multimodal imaging, this study highlights the importance of the hippocampus during premise integration and supports compensatory role of the hippocampal network during a logical reasoning task among older adults.

Overview of Mental Models research using bibliometric indicators

The Mental Model concept has evolved from being a representation of reality to which we apply formal logic, to a type of logic with which we make decisions, learn, and adapt. This work uses bibliometric indicators to describe research on Mental Models from 1997 to 2017. The results show progressive growth since the late 1990s and a stationary trend starting in 2010. The existing research is dominated by the fields of individual and organizational psychology as well as education. Since 2007, a corpus of research (works that continue or are based on previous work) has been developed around the themes of memory, cognition, interpretation, and Johnson-Laird's work. In the late 2000s, another possible corpus emerged around team work. It is recommended to develop similar research in specific areas.

The Analytic Truth and Falsity of Disjunctions

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its 'partition': A and B, A and not-B, not-A and B, not-A and not-B, as 'possible' or 'impossible' in ways that bore out the difference between inclusive disjunctions ('or both') and exclusive disjunctions ('but not both'). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer 'mirror-image' evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.

The Dialogical Entailment Task

In this paper, a critical discussion is made of the role of entailments in the so-called New Paradigm of psychology of reasoning based on Bayesian models of rationality (Elqayam & Over, 2013). It is argued that assessments of probabilistic coherence cannot stand on their own, but that they need to be integrated with empirical studies of intuitive entailment judgments. This need is motivated not just by the requirements of probability theory itself, but also by a need to enhance the interdisciplinary integration of the psychology of reasoning with formal semantics in linguistics. The constructive goal of the paper is to introduce a new experimental paradigm, called the Dialogical Entailment task, to supplement current trends in the psychology of reasoning towards investigating knowledge-rich, social reasoning under uncertainty (Oaksford & Chater, 2019). As a case study, this experimental paradigm is applied to reasoning with conditionals and negation operators (e.g. CEM and wide and narrow-scope negation). As part of the investigation, participants' entailment judgments are evaluated against their probability evaluations to assess participants' cross-task consistency over two experimental sessions.