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 generally found that people 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 judgements about general conditionals. In Experiment 1, for truth judgements, people evaluated a general conditional as "true" in sets containing p & q cases but no p & ¬q, and "true" judgements depended only on P(q|p). In Experiment 2, for possibility judgements, 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.

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.

The relative difficulty of negations of conjunctions and disjunctions-a mental model perspective.

A current issue in propositional reasoning is which of negated disjunctions and conjunctions are more difficult to understand. Using the possibility generation and evaluation tasks, we investigated how people make possibility inferences from negated compound assertions such as not (A and B) and not (A or B). We derive 4 different strategies of negation from the mental model theory (the enumerative negation, the eliminative negation, the element negation, and the clause negation) to predict the relative difficulty of possibility inference from not (A and B) and not (A or B). The results of three experiments convergently demonstrate that possibility inference from not (A or B) is harder than that from not (A and B). Moreover, an interpretation of negation as the complement of the set of possibilities allowed by a compound assertion is in line with the results of not (A and B) rather than not (A or B). The overall results favor the clause negation strategy over the other strategies.

A situation-modulated minimal change account for causal inferences about causal networks.

Although causal Bayes networks are applicable to examining causal inferences about different static objects and about a changing object with different states, previous studies investigated the former, but not the latter. We propose a situation-modulated minimal change account for causal inferences. It predicts that dynamic situations are more likely to elicit minimal revisions on causal networks and adherence to the Markov assumption than static situations. Two experiments were conducted to investigate qualitative causal inferences about causal networks with binary and numerical variables, respectively. It was found that qualitative causal inferences were more likely to adhere to the Markov assumption in dynamic situations than in static situations. This finding supports the situation-modulated minimal change account rather than the other alternative accounts. We conclude that dynamic situations are more likely to elicit minimal revisions on causal networks and adherence to the Markov assumption than static situations. This conclusion is beyond the previous predominant view that causal inferences are apt to violate the Markov assumption.

Different responses in metallothionein gene expression and antioxidative enzyme activity lead to more ROS accumulation in rice exposed to Tl(III) than to Tl(I).

This is the first study to investigate the reduction mechanism of Tl (III) to Tl(I) in the presence of plants, especially rice. Smaller plant density could effectively reduce the content of organic acids in the hydroponic system to keep the stability of Tl(III). As the plant density was reduced from 40 seedlings to 10 seedlings in 100 mL Tl(III) solution, the content of oxalate was declined to one-third of the original, and the ratio of Tl(III)/total Tl was increased from 39.6% to 81.0% in the first 2 h treatment. Then the differences in antioxidant capacity of rice exposed to the two Tl species were studied. The contents of malondialdehyde (MDA), hydrogen peroxide (H2O2) and superoxide anion (O2˙-) of rice roots exposed to Tl(III) were all higher than those to Tl(I). Meanwhile, the catalase (CAT) activity was significantly depressed and peroxidase (POD) was increased by Tl(III), whereas superoxide dismutase (SOD) showed a rise in both Tl(I) and Tl(III) with no significant difference between them. The expression of metallothionein gene OsMT1a to Tl(I) was upregulated to 255.5 times of Tl(III) though OsMT2c was downregulated to 0.39 times of Tl(III). Overall, the different responses in metallothionein gene expression and antioxidative enzyme activation might result in more ROS accumulation to rice roots by Tl(III) treatment than those by Tl(I).

The Preference for Joint Attributions Over Contrast-Factor Attributions in Causal Contrast Situations.

A current issue about causal attribution is whether people take simple contrast-factor attributions or complex joint attributions in contrast situations. For example, a stone does not dissolve in water and a piece of salt dissolves in water. That the piece of salt dissolves in water is due to: (A) the influence of the piece of salt; (B) the influence of the water; (C) the joint influence of the piece of salt and the water. We propose a mechanism-based sufficiency account for such questions. It argues that causal attributions are guided by mechanism-based explanatory sufficiency, and people prefer a mechanism-based attribution with explanatory sufficiency. This account predicts the sufficient joint attribution (the C option), whereas the conventional covariation approach predicts the contrast-factor attribution (the A option). Two experiments investigated whether contrast situations affect causal attributions for compound causation with explicit mechanism information and simple causation without explicit mechanism information, respectively. Both experiments found that in both the presence and absence of contrast situations, the majority of participants preferred sufficient joint attributions to simple contrast-factor attributions regardless of whether explicit mechanism information was present, and contrast situations did not affect causal attributions. These findings favor the mechanism-based sufficiency account rather than the covariation approach and the complexity account. In contrast situations, the predominance of joint attributions implies that explanatory complexity affects causal attributions by the modulation of explanatory sufficiency, and people prefer mechanism-based joint attributions that provide sufficient explanations for effects. The present findings are beyond the existing approaches to causal attributions.

Evidence for the Jeffrey Table.

Conditionals statements are a common and necessary component in natural languages. The research reported in this paper is on a fundamental question about singular conditionals. Is there an adequate account of people's truth, falsity, and credibility (probability) judgments about these conditionals when their antecedents are false? Two experiments examined people's quantitative credibility ratings and qualitative truth and falsity judgments for singular conditionals, if p then q, given false antecedent, not-p, cases. The results demonstrate that, when relevant knowledge about the conditional probability of q given p, P(q|p), is available to participants in not-p cases, they tend to make credibility ratings based on P(q|p), and to make "true" (or "false") judgments at a high (or low) level of these credibility ratings. These findings favor the Jeffrey table account of these conditionals over the other existing accounts, including that of the de Finetti table.

What Is Transferred in Causal Generalization Across Contexts?

The covariation and causal power account for causal induction make different predictions for what is transferred in causal generalization across contexts. Two experiments tested these predictions using hypothetical scenarios in which the effect of an intervention was evaluated between (Experiment 1) or within (Experiment 2) groups. Each experiment contained a manipulation of ΔP, power and their combination. Both experiments found that causal transfer was determined by ΔP rather than causal power. The overall transfer pattern supports ΔP transfer account rather than the other transfer accounts. Causal transfers based on ΔP are irrational, violating the coherence criterion of the causal power framework. The ΔP transfer is consistent with previous findings that ΔP is a main mental non-normative measure of causal strength in causal induction.

The dual reading of general conditionals: The influence of abstract versus concrete contexts.

A current main issue on conditionals is whether the meaning of general conditionals (e.g., If a card is red, then it is round) is deterministic (exceptionless) or probabilistic (exception-tolerating). In order to resolve the issue, two experiments examined the influence of conditional contexts (with vs. without frequency information of truth table cases) on the reading of general conditionals. Experiment 1 examined the direct reading of general conditionals in the possibility judgment task. Experiment 2 examined the indirect reading of general conditionals in the truth judgment task. It was found that both the direct and indirect reading of general conditionals exhibited the duality: the predominant deterministic semantic reading of conditionals without frequency information, and the predominant probabilistic pragmatic reading of conditionals with frequency information. The context of general conditionals determined the predominant reading of general conditionals. There were obvious individual differences in reading general conditionals with frequency information. The meaning of general conditionals is relative, depending on conditional contexts. The reading of general conditionals is flexible and complex so that no simple deterministic and probabilistic accounts are able to explain it. The present findings are beyond the extant deterministic and probabilistic accounts of conditionals.

The influence of category representations on exemplar generation.

The present study examined the influence of category representations on exemplar generation, which has been neglected in previous category research. An experiment on college students manipulated the category representation of insects in three conditions (prototypes, exemplars, and the hybrid of prototypes and exemplars). Participants were asked to generate as many exemplars as possible. The results demonstrate that category representations affect and constrain exemplar generation. The new findings are as follows. In the prototype and hybrid conditions with the prototype representation, people tend to generate more valid exemplars by using the prototype mutation mechanism, and exemplar generation conforms to the family resemblance structure. Exemplar generation in the hybrid condition is additionally constrained by known exemplars. In the exemplar condition, people tend to generate fewer valid exemplars by using miscellaneous strategies, and their exemplar generation may not conform to the family resemblance structure.