The reading of external negated disjunctions (a disjunction as a clause is externally negated) is an interdisciplinary issue addressed by logic, linguistics, and psychology. For external negated disjunctions, we investigated how their possibility judgments varied with their two expression forms: NTSs (not-true sentences) with the form It is not true that p or q or both versus DSs (deny-sentences) with the form Someone denied that p or q or both). We propose the semantic negation scope account for the question with the hypothesis of the effect of expression form of negation that a NTS will more often elicit the weak local negation strategy that people consider cases negating at least one of the disjuncts as possible, and judge p¬q, ¬pq, and ¬p¬q as possible; while a DS will more often elicit the strong global negation strategy that people consider only cases negating all disjuncts as possible, and judge only ¬p¬q as possible. Experiments 1 and 2 tested the hypothesis in verbal and pictural scenarios, respectively. Both experiments exhibited the effect of expression form of negation that DSs more often elicited the strong global negation strategy, while in conversational and non-conversational contexts, NTSs more often elicited the weak local negation strategy, as favoring the semantic negation scope account over the alternative accounts. The effect of expression form of negation suggests that there seems no unified mental mechanism of the reading of external negated disjunctions with different expression forms.

An epistemic relative necessity account is proposed to treat nonmodal deductive reasoning as modal reasoning. It assumes that an epistemically valid conclusion from the factual premises is pragmatically necessary relative to the premises. Three studies on modal Modus Ponens problems (with the form: given the premises of p and if p then q, individuals were asked to judge whether the conclusion is "necessarily q," "q," or "possibly q") revealed (1) Participants generally defaulted to interpreting arbitrary conditionals "if p then q" as "if p then must q." (2) Modal MP problems without retrievable counterexamples to conditionals tended to elicit inferences "necessarily q" rather than "q." (3) The influence of level of relevance in conditionals (arbitrary vs. causal conditionals) on modal inferences was modulated by whether causal conditionals had retrievable counterexamples: Causal conditionals with retrievable counterexamples elicited more "possibly q" inferences (belief bias responses) and fewer "necessarily q" inferences than arbitrary and causal conditionals without retrievable counterexamples. The overall response pattern favors only the epistemic relative necessity account, indicating that a mentally valid nonmodal deductive inference can be transformed into a modal inference including the modal word "necessary" in the conclusion. Our research bridges linguistic and psychological research on epistemic necessity.

We propose an integrated semantic-pragmatic account predicting the relative reading of necessary conditionals (NCs) (with two typical expression forms: p only if q vs. not-p unless q). It assumes that the reading of NCs is the joint effect of the semantic factor (q being necessary for p is context-independent) and the pragmatic factor (whether q is sufficient for p is context-dependent), and so varies with level of abstraction (abstract vs. concrete materials) in content. Three experiments used equivalence judgment tasks, possibility judgment tasks, and conditional reasoning tasks, respectively, to investigate how expression form and level of abstraction affect the reading of Chinese NCs. Experiment 1 established the equivalence between the two expression forms. Experiment 2 found that response patterns in conditional reasoning about NCs more often indicated the dual interpretation (q is both necessary and sufficient for p) in abstract materials than in concrete ones. Experiment 3 found that patterns of possibility judgments of four cases under NCs more often indicated the dual interpretation in abstract materials than in concrete ones. Overall, abstract NCs more often meant the dual interpretation than concrete NCs did, regardless of expression form. The present findings support the integrated semantic-pragmatic account rather than the mental model theory.

How people make inferences between disjunctions and conditionals is a current important question that can test mental logic and mental model theories in propositional reasoning. We propose a dual process account that predicts and integrates diverse reasoning strategies in inferences between disjunctions and conditionals. Two experiments revealed that there were obvious individual differences in reasoning strategies, which led to individual differences in reasoning performances. In particular, the syntactic meaning contrast heuristic dominated inferences in general conditions, whereas knowledge modulation heuristics such as contradiction interpretations and prior belief biases dominated inferences in particular conditions. These heuristics trumped the compatibility heuristic and the analytic strategies of mental logic and mental model theories. Competitions among these diverse reasoning strategies led to symmetries and asymmetries between inferences between disjunctions and conditionals. The overall pattern of individual differences in reasoning strategies favors the dual process account over the other accounts. The finding of the diverse reasoning strategies suggests that there is no single reasoning mechanism that underpins all inferences between disjunctions and conditionals.

College students give true judgment routinely, logicians can infer modal inferences, i.e., inferences that concern three alethic modalities; necessary (⸧), possible (◊), and impossible (⟢) from the premises that are logically consistent and incompatible. To achieve the desired results, logicians have intermingled alethic modalities with logical consistency and incompatibility, i.e., necessary consistent, impossible incompatible, possible consistent, or possible incompatible, and write them in classical modal logic as ⸧C (necessary consistent), ◊C (possible consistent) or ◊I (possibly incompatible) and ⟢I (impossible incompatible). M paradigm [Modality, Mental logic theory (MLT), and Mental model theory (MMT)] have been built to enlighten this truth logic. The basic idea of this study is to examine the theory; how do students judge whether two or more different propositions are possible? and, whether their judgment is true. Truth logic is used to construct some principles that help to justify the above theory. First, inferences have either ◊C/ ◊I or ⸧C but assertions are consistent. Second, each ◊C/ ◊I inference and premise is evaluated for both single and double model assertions, and they have consistency (i.e., ⸧C/◊C) and incompatibility (i.e., ◊I or ⟢I). As logicians have predicted, students mostly endorse inferences as ◊C/ ◊I rather than ⸧C and the ⟢I rate is higher in multi-model assertions. Syllogistic logical reasoning with conditionals (if, then...), conjunctions (and), disjunctions (or), and quantifiers “all” and “some” have been used in the M paradigm to evaluate predictions. Moreover, a computational program and experimental studies have strongly supported the all given principles and predictions.

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.

A current issue in natural language semantics and the psychology of reasoning is how people make inferences between two disjunctive sentences (e.g., inferences between There is A or B or C and There is A or B; inferences between There is at least one of A, B, and C and There is at least one of A, B, C, and D) with two different sets of elements. The interdisciplinary question whether different linguistic forms (OR versus quantifier rule frames) of equivalent disjunctive sentences make a difference to human inferences between two disjunctive sentences with two different sets of elements can distinguish between syntactic and semantic accounts for reasoning. Classical logic, the Bayesian approach, the original and revised mental models theory all answer “no” to the question. Alternatively, an epistemic rule relation account based on comparing explicit rules (that is, syntactic gestalts) of premise and conclusion sentences answers “yes” to the question. Three experiments found the effect of rule frames that quantifier frames elicited more correct inferences than OR frames, and these two rule frames elicited opposite response patterns. This finding favors only the epistemic rule relation account, and suggests the general implication that inferences between two compound sentences may primarily be based on the epistemic rule relation between both, which is modulated by rule frame.Keywords: inferences between disjunctive sentences; rule frame; or; at least one; the epistemic rule relation account; framing effects

How people make inferences between disjunctions and conditionals is a current important question that can test existing main psychological accounts for propositional reasoning.In order to test these accounts, one experiment investigated how relations and inference directions affect human inferences between both.Tworelationships between two basic components（A and B）havebeenstudied, andtheyare inclusive disjunctions and exclusive disjunctions.There were also two inference directions in disjunctions（e.g.,A or B;not-A or B）and conditionals（e.g.,if not-A then B;if A then B）havebeenstudied, and they are disjunction-to-conditional and conditional-to-disjunction.It was found that participants’ inferenceswere symmetric between the two inference directions in compatible relations and incompatible relations where two basic components were on different dimensions, but not in the other relations.Belief biases also affected participants’ inferences.Which of the two inference directions was easier depended on relations between two basic components, and so was relative.The present overall response pattern is beyond all the existing accounts for inferences between disjunctions and conditionals.The competition between the special knowledge heuristic and the general syntactic meaning comparison heuristic proposed by the author can explain the present dominant responses.

In reasoning about common cause networks, given that a cause generates an effect, people often need to infer how likely the cause generate another effect. This causal generalization question has not systematically been investigated in previous research. We propose the information integration account for causal generalizations in uncertain casual networks with dichotomized continuous variables. It predicts that causal generalization is the joint function of conditional probabilities of causal links and cause strength indicated by the proportion of present collateral effects. Two experiments investigated causal generalizations in uncertain causal networks with and without probability distributions, respectively. It was found that in the presence of probability distributions there was the joint effect of conditional probability and cause strength on causal generalization; in the absence of probability distributions causal generalization depend only on cause strength. The overall response pattern favors the information integration account over the other alternative accounts.

In the psychology of propositional reasoning and psycholinguistics, few previous studies have investigated how people read the negation of a general disjunction referring to a definite narrow-scope set of objects (for a set with limited objects, it is not true that xs are p or q). We develop some alternative accounts for the negation. The original and revised mental model theory make contradictory predictions for the negation. The probabilistic violation account interprets it as the probabilistic violation of the general disjunction by introducing nonnegligible exceptions. A rule violation account based on the default rule reading of generics in psycholinguistics interprets it as the rule violation of the general disjunction by introducing exceptions. Four experiments investigated the reading of negated general disjunctions referring to definite narrow-scope sets in 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. This implies that people tend to understand the general disjunction as the deterministic universal rule, and interpret the negated general disjunction as the qualitative violation of the rule by introducing exceptions. These findings favor the rule violation account over the other accounts. The present overall response pattern is consistent with the default universal rule interpretation of generic sentences referring to definite narrow-scope sets predicted by the relativity principle in psycholinguistics that reading generics as probabilistic or deterministic is relative, depending on background knowledge or contexts. The relative reading of general disjunctions is beyond existing simple deterministic and probabilistic accounts of compound propositions in propositional reasoning.

For the modal meanings of conditionals with the form if p then q, existing psychological accounts imply different modal meanings of if p then q. For instance and categorical modal inferences from conditionals in sampling problems, the basic principle is that whether or not a set includes some case determines whether or not an instance randomly drawn from the set is possibly this case. One experiment investigated the relationship between instance and categorical modal inferences from conditionals. The results demonstrate that (1) cases pq and p¬q tend to elicit consistent response patterns conforming to the basic principle, but cases ¬pq and ¬p¬q tend to elicit inconsistent response patterns violating the basic principle; (2) the inconsistent response pattern of not-p cases can be explained by the pragmatic heuristic that no evidence can rule out that not-p cases are possible; (3) the overall pattern of modal inferences is beyond each existing theory. Alternatively, we propose a revised suppositional theory (ST3) integrating the constraint of the truth conditions of conditionals in the Jeffrey table and the pragmatic heuristic. It can explain the overall pattern of modal inferences. Overall, a true conditional requires that pq is possible and p¬q is impossible for the instance of the true conditional, but not that not-p cases are possible. This favors the pragmatic heuristic account with ST3 over the semantic compatibility assumption in mental models theories.

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.

Conditionals are extensively used in science and everyday life. A current issue about conditionals is what cases a true conditional (if p then q) implies, or what case is an instance that the conditional refers to. This is the reference inference problem of conditionals. We explore a specific reference inference problem as follows. Given that a specific conditional (e.g., If the card is red, then it is round) is true of one instance, people are asked to judge whether the instance is, is possibly, or is not one of the four truthtable cases (pq, p¬q, ¬pq and ¬p¬q) (where, “¬” = not). We refer to such problems as the instance inference task of conditionals. Its inferential direction is contrary to that of the truth evaluation task in the previous literature that ask people to judge whether a conditional is true or false, given that an instance is one of the four truth-table cases [1-5].

A current dispute in the psychology of conditionals is which possibility is necessary for basic conditionals such as if p then q. There are three accounts with different predictions about the question. The original model theory predicts that if p then q means the disjunction of three possibilities: possibly pq or possibly ¬pq or possibly ¬p¬q ( ¬ = “not”), in which each is unnecessary. The revised model theory predicts that it means the conjunction of the three possibilities, in which each is necessary. The suppositional theory predicts that people interpret it as a hypothetical test based on the conditional probability of p given q, in which only the pq possibility is necessary. Two experiments investigated possibility and truth judgments about basic conditionals given sets that consist of one or more of the four truth table cases of basic conditionals. The results demonstrate that both judgments approximate to the prediction of the suppositional theory rather than the original and revised model theory, and so people show the suppositional interpretation of basic conditionals, in which only the pq possibility is necessary for basic conditionals. Only the pq possibility is necessary for judging a basic conditional true. A true basic conditional mentally implies that only the pq possibility is necessary. These findings support the suppositional theory, but not the original and revised model theory.

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.

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.

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.

The author investigated the relationship between possibility and necessity inferences from general conditionals (e.g., If a card is red, then it is round). An experiment examined how people reason about what cases are possible or necessary under a general conditional. Participants were asked to infer whether each truth-table cases (pq, p¬q, ¬pq and ¬p¬q) (¬ = not) must be in the set of cases under a true general conditional, and whether the combinatorial sets of the four truth-table cases are possible under the conditional. The test order of necessity and possibility questions was varied with the NP (necessity/possibility questions) and PN (possibility/necessity questions) group. The findings are as follows. The test order did not affect the relationship between possibility and necessity inferences for each of p¬q, ¬pq and ¬p¬q cases. It affected the relationship between necessity inferences for pq cases and possibility inferences for the sets including only ¬pq or ¬p¬q cases. The NP group more often showed the contradiction between these two inferences than the PN group. The existing main accounts of conditionals are unable to explain the contradiction. Alternatively, the author proposes an inference dissociation account for it.

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.