The Causal Structure of Utility Conditionals

The psychology of reasoning is increasingly considering agents' values and preferences, achieving greater integration with judgment and decision making, social cognition, and moral reasoning. Some of this research investigates utility conditionals, ‘‘if p then q’’ statements where the realization of p or q or both is valued by some agents. Various approaches to utility conditionals share the assumption that reasoners make inferences from utility conditionals based on the comparison between the utility of p and the expected utility of q. This article introduces a new parameter in this analysis, the underlying causal structure of the conditional. Four experiments showed that causal structure moderated utility‐informed conditional reasoning. These inferences were strongly invited when the underlying structure of the conditional was causal, and significantly less so when the underlying structure of the conditional was diagnostic. This asymmetry was only observed for conditionals in which the utility of q was clear, and disappeared when the utility of q was unclear. Thus, an adequate account of utility‐informed inferences conditional reasoning requires three components: utility, probability, and causal structure.     

Concessive and semifactual interpretations during reasoning with multiple conditionals

The present research evaluates how people integrate factual ‘if then’ and semifactual ‘even if’ conditional premises in an inference task. The theory of mental models establishes that semifactual statements are represented by two mental models with different epistemic status: ‘A & B’ is conjectured and ‘not-A & B’ is presupposed. However, following the principle of cognitive economy in tasks with a high working memory load such as reasoning with multiple conditionals, people could simplify the deduction process in two ways, by discarding: (a) the presupposed case and/or (b) the epistemic status information. In Experiment 1 and Experiment 2, we evaluated each of these hypotheses. In Experiment 1, participants make inferences from two conditionals: two factual conditionals or one factual and one semifactual, with different representations. In Experiment 2, participants make inferences with a factual conditional followed by two different semifactual conditionals that share the same representations but differ in their epistemic status. Accuracy and latency data suggest that people think of both the conjectured and the presupposed situations, but do not codify the epistemic status of either when the task does not require it. The results are discussed through theoretical predictions about how people make inferences from different connected conditionals.     

Transmission Failure Explained1

In this paper I draw attention to a peculiar epistemic feature exhibited by certain deductively valid inferences. Certain deductively valid inferences are unable to enhance the reliability of one’s belief that the conclusion is true—in a sense that will be fully explained. As I shall show, this feature is demonstrably present in certain philosophically significant inferences—such as GE Moore’s notorious ‘proof’ of the existence of the external world. I suggest that this peculiar epistemic feature might be correlated with the much discussed phenomenon that Crispin Wright and Martin Davies have called ‘transmission failure’—the apparent failure, on the part of some deductively valid inferences to transmit one’s justification for believing the premises.     

Mental Files and Rational Inferences

Abstract

My goal in this paper is to discuss the ‘Fregean’ account of inferences proposed by Recanati in his Mental Files (Oxford University Press, 2012). I raise the following dilemma for the mental files theory. (a) If the premises of certain inferences involve ‘the same file’ in a strict sense of the expression, then files cannot play the role of modes of presentation. (b) If, on the other hand, the files involved in the premises are ‘the same’ only in a loose sense, then the notion of file sameness plays no role in accounting for rational inferences, contra Recanati’s Fregean account.     

条件推理的语义关系表达形式效应

作者用以大学生为被试的实验考察, 基本条件句语义关系表达形式(充分关系、必要关系和析取关系表达形式)和作为心理模型外显建构的可能性判断任务对条件推理的可能影响。实验结果发现, 条件推理的语义关系表达形式效应显著, 条件句语义关系表达形式对被试条件推理有显著的影响, 条件推理成绩随条件句语义关系表达的外显程度增加而增加; 被试在可能性判断任务中对条件句所含心理模型的外显建构并没有明显改善条件推理的成绩; 在有可能性判断任务条件下, 被试外显心理模型建构的成绩变化模式并不能一致地预测条件推理成绩的变化模式。这些结果说明, 人们的条件推理可能并不是完全基于心理模型建构, 而是还受对条件句前后件之间语义关系理解的影响; 条件句表达形式中语义关系的外显内隐模式影响对条件句语义关系的知觉理解难易, 从而影响相应条件推理的成绩。     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.     

Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models

We report four experiments investigating conjunctive inferences (from a conjunction and two conditional premises) and disjunctive inferences (from a disjunction and the same two conditionals). The mental model theory predicts that the conjunctive inferences, which require one model, should be easier than the disjunctive inferences, which require multiple models. Formal rule theories predict either the opposite result or no difference between the inferences. The experiments showed that the inferences were equally easy when the participants evaluated given conclusions, but that the conjunctive inferences were easier than the disjunctive inferences (1) when the participants drew their own conclusions, (2) when the conjunction and disjunction came last in the premises, (3) in the time the participants spent reading the premises and in responding to given conclusions, and (4) in their ratings of the difficulty of the inferences. The results support the model theory and demonstrate the importance of reasoners' inferential strategies.     

Real Objects Can Impede Conditional Reasoning but Augmented Objects Do Not

In this study, Knauff and Johnson‐Laird's (2002) visual impedance hypothesis (i.e., mental representations with irrelevant visual detail can impede reasoning) is applied to the domain of external representations and diagrammatic reasoning. We show that the use of real objects and augmented real (AR) objects can control human interpretation and reasoning about conditionals. As participants made inferences (e.g., an invalid one from "if P then Q" to "P"), they also moved objects corresponding to premises. Participants who moved real objects made more invalid inferences than those who moved AR objects and those who did not manipulate objects (there was no significant difference between the last two groups). Our results showed that real objects impeded conditional reasoning, but AR objects did not. These findings are explained by the fact that real objects may over‐specify a single state that exists, while AR objects suggest multiple possibilities.     

Disjunctive illusory inferences and how to eliminate them

The mental model theory of reasoning postulates that individuals construct mental models of the possibilities in which the premises of an inference hold and that these models represent what is true but not what is false. An unexpected consequence of this assumption is that certain premises should yield systematically invalid inferences. This prediction is unique among current theories of reasoning, because no alternative theory, whether based on formal rules of inference or on probabilistic considerations, predicts these illusory inferences. We report three studies of novel illusory inferences that depend on embedded disjunctions—for example, premises of this sort: A or else (B or else C). The theory distinguishes between those embedded disjunctions that should yield illusions and those that should not. In Experiment 1, we corroborated this distinction. In Experiment 2, we extended the illusory inferences to a more stringently controlled set of problems. In Experiment 3, we established a novel method for reducing illusions by calling for participants to make auxiliary inferences.     

On the generation and evaluation of inferences from single premises

A theory of how individuals construct mental models to draw inferences from single premises was tested in three experiments. Experiment 1 confirmed a counterintuitive prediction that it is easier to generate inferences between conditionals and disjunctions than it is to evaluate them. Experiment 2 replicated this finding, but an advantage found in the first experiment for conditional-to-disjunction over disjunction-to-conditional inferences was removed with different sentence contents. Experiment 3 showed that disjunction-to-conditional inferences were facilitated when premises expressed familiar indicative relations, whereas conditional-to-disjunction inferences were facilitated when premises expressed causal relations. The results indicate that small changes in task format can have large effects on the strategies that people use to represent and reason about different sentential connectives. We discuss the potential for theories other than mental models to account for these results. We argue that, despite the important role played by single-premise inferences in paraphrasing logical forms during inference, mental logic theories cannot account for the results reported here.     

What Do Easy Inferences Get Us?

In Ontology Made Easy (2015), I defend the idea that there are ‘easy’ inferences that begin from uncontroversial premises and end with answers to disputed ontological questions. But what do easy inferences really get us? Bueno and Cumpa (this journal, 2020) argue that easy inferences don’t tell us about the natures of properties—they don’t tell us what properties are. Moreover, they argue, by accepting an ontologically neutral quantifier we can also resist the conclusion that properties or numbers exist. Here I address these two issues in turn—in ways that help clarify both the scope and results of easy ontology. First, it is important to see that easy inferences were never intended to address modal questions. Modal questions are addressed by a different part of the total deflationary view—modal normativism. So understood, metaphysical modal questions nonetheless do not provide a remaining area for serious metaphysical inquiry. Second, I argue that we have reason to resist adopting an ontologically neutral quantifier, if we aim to answer ontological questions (without begging the question). Addressing these issues helps to clarify both what does (and does not) follow from easy inferences, and how they form part of a larger deflationary metametaphysical view.     

Bias in Conditional Inference: Implications for Mental Models and Mental Logic

Three experiments are reported in which subjects are given the opportunity to make any of the four inferences associated with conditional statements: modus ponens (MP), denial of the antecedent (DA), affirmation of the consequent (AC), and modus tollens (MT). The primary purpose of the research was to establish the generality and robustness of polarity biases that may be occasioned by systematic rotation of negative components in the conditional rules. In Experiments 1 & 2, three forms of conditionals were used: “if (not) p then (not) q”, “(not) p only if (not) q” and “(not) q if (not) p”. Experiment 1 used a conclusion evaluation task, whereas Experiment 2 used a conclusion production task. In Experiment 3, thematic conditionals were presented with and without a preceding scenario.

The biases investigated were (a) affirmative premise bias—the tendency to draw more inferences from affirmative premises and (b) negative conclusion bias—the tendency to draw more inferences with negative conclusions. The suggestive evidence for affirmative premise bias in the literature was not supported: very little evidence was found for it in the current experiments. Robust findings of negative conclusion bias were, however, found across the three experiments, although the bias was mostly restricted to DA and MT inferences. This suggests that the bias is best regarded as a difficulty with double negation.

The results are discussed with respect to both the mental logic and mental model accounts of propositional reasoning. Neither theory as currently formulated can explain all of our findings, although a plausible revision of each is considered.     

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.     

Effects of order of presentation on conditional reasoning

ABSTRACT

The main goal of this research is to study whether or not the order of presentation of the premises in a logical argument form, such as a conditional reasoning task, could affect the processing time of premises and conclusion and the conclusions that participants accept as valid in an evaluation task. One experiment is reported in which participants are asked to evaluate computer-presented conditionals. Half of the problems were presented in traditional order (“if p then q, p, therefore q”) and half in inverse order (“p, if p then q, therefore q”). The experiment showed that there was an order effect in processing the premises and conclusion: participants took longer to read the premises in traditional order than in inverse order, but they took longer to read the conclusion in inverse order than in traditional order. The finding is discussed with respect to the main theories of conditional reasoning.     

Deductive schemas with uncertain premises using qualitative probability expressions

The new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Word for word: Multiple lexical access in speech production

We report an experiment in which we test the possible influence of the tense of the verb and explicit negatives with indicative conditionals. We tested the effects of systematically negating the constituents of four fundamental inferences based on conditionals in three different tenses (present tense, past tense, future tense): Modus Ponens (i.e., inferences of the form: if p then q; p; therefore q), Modus Tollens (if p then q; not-q; therefore not-p), Affirmation of the Consequent (if p then q; q; therefore p), and Denial of the Antecedent (if p then q; not-p; therefore not-q). The latter two inferences are invalid for true conditionals, but are valid for bi-conditionals (if, and only if, p then q). The participants drew their own conclusions from premises about letters and numbers on cards. We discuss the results in relation to an affirmation premise bias, a negative conclusion bias, and a double negation effect. We outline the importance of our findings for theories about conditional and counterfactual thinking.     

A psychological study of unconnected conditionals

Unconnected conditionals, also called irrelevant conditionals, are sentences of form if A, C, whose antecedent and consequent bear no connection. According to the main theories of conditional reasoning, the truth or high probability of an antecedent and a consequent is sufficient to make true or highly probable the corresponding conditional. We tested this assumption and showed that it does not hold for unconnected conditionals. Furthermore, we investigated experimentally the factors which favour the endorsement of irrelevant conditional constructions and found that this rate increases when an analogy can be built between the antecedent and the consequent or when the conditional is asserted before its components.     

On problems of context and attribution in verbal reasoning

Investigated the effect of the verb on inferences in reasoning tasks with conditionals. Subjects were 60 pupils, both male and female, aged 17 to 18 years. Six verbs (buy, have, understand, ignore, hate, avoid) served as independent variables in conditional tasks consisting of two premises. The results which are statistically, highly significant, show an effect due to the verb depending upon the logical form of the task (2Î = 86.1, df= 30). indicate that certain semantic characteristics implicit in verbs determine the way in which a reasoning task is interpreted. A second experiment investigated why verbs differ in this way. Interviews were carried out with subjects using the verbs ‘buy’ and ‘ignore’. It is suggested that implicit meanings acquired through processes of social attribution play an essential role in verbal reasoning. In the present case, such attributions concern the depositional and episodic character of verbs and appear to be responsible for the interpretation of the premises of our tasks. It is concluded that any logical model aiming at an adequate representation of language in reasoning must take these implicit social attributions into account.     

The Logic of Dominance Reasoning

The logic of dominance arguments is analyzed using two different kinds of conditionals: indicative (epistemic) and subjunctive (counter‐factual). It is shown that on the indicative interpretation an assumtion of independence is needed for a dominance argument to go through. It is also shown that on the subjunctive interpretation no assumption of independence is needed once the standard premises of the dominance argument are true, but that independence plays an important role in arguing for the truth of the premises of the dominance argument. A key feature of the analysis is the interpretation of the doubly conditional comparative "I will get a better outcome if A than if B" which is taken to have the structure "(the outcome if A) is better than (the outcome if B)".