Logic of primary-conditionals and secondary-conditionals

Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establish the minimum system C2L _m of primary-conditionals and secondary-conditionals, and then prove some of the formal theorems of the system which have important intuitive meanings. Secondly, the authors constructed the neighborhood semantics, prove the soundness of C2L _m, introduce a general concept of canonical model by the neighborhood semantics, and then prove the completeness of C2L _m by the canonical model. Finally, according to the technical results of the minimum system C2L _m, the authors discuss some of the important problems concerning primary-conditionals and secondary-onditionals. __________ Translated from Luoji Yu Renzhi 逻辑与认知 (Logic and Cognition) (online journal), 2004 (3)     

Framing experts' (dis)agreements about uncertain environmental events

Agreements and disagreements between expert statements influence lay people's beliefs. But few studies have examined what is perceived as a disagreement. We report six experiments where people rated agreement between pairs of probabilistic statements about environmental events, attributed to two different experts or to the same expert at two different points in time. The statements differed in frame, by focusing on complementary outcomes (45% probability that smog will have negative health effects vs. 55% probability that it will not have such effects), in probability level (45% vs. 55% probability of negative effects), or in both respects. Opposite frames strengthened disagreement when combined with different probability levels. Approximate probabilities can be “framed” in yet another way by indicating reference values they are “over” or “under”. Statements that use different directional verbal terms (over vs. under 50%) indicated greater disagreement than statements with the same directional term but different probability levels (over 50% vs. over 70%). Framing and directional terms similarly affected consistency judgments when both statements were issued by the same expert at different occasions. The effect of framing on perceived agreement was significant for medium (10 and 20 percentage points) differences between probabilities, whereas the effect of directional term was stable for numerical differences up to 40 percentage points. To emphasize agreement between different estimates, they should be framed in the same way. To accentuate disagreements or changes of opinion, opposite framings should be used.     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.     

A survey on adverse incidents in legal psychology studies: Reflections on ethics review

Ethics committees (ECs) regulate research activities to maintain research participants' autonomy and to protect them from harm and injury. No research to date attempted to establish how much risk is involved in social‐science research. Using a survey approach, we set out to estimate the risk of being involved in an incident for research participants in legal psychology and assessed researchers' views of ECs. Fifty‐nine of 188 respondents (31%) stated that they had experienced one or more incidents with a participant. The estimated risk of being involved in an incident was one to three per 10,000 participants, which according to biomedical standards defines a rare risk. Although some researchers were satisfied with their EC, the general tenor was one of discontent due to conservative decision‐making, lacking expertise, and overstepping demands. Whether ECs succeed in protecting participants from loss of autonomy, harm and injury are unknown but are open to empirical research.     

Compositionality and the Prospect of a Pluralistic Semantic Theory

A semantic theory is committed to semantic monism just in case every particular semantic property posited by the theory is a member of the same kind. The commitment to semantic monism appears to draw some support from the need to provide a compositional semantics, since taking a single kind of semantic property as key to a semantic theory affords a uniform pattern on the basis of which the meaning of any given sentence can be compositionally determined. This line of support highlights a tension between the principle of compositionality and taking a more pluralistic approach to semantic theorizing. In this essay, that tension is relieved, leaving open the prospect of a pluralistic semantic theory that observes the principle of compositionality.     

Getting scarred and winning lotteries: effects of exemplar cuing and statistical format on imagining low‐probability events

Three experiments tested the exemplar cuing and frequency format accounts of how the ‘imaginability’ of low‐probability events is enhanced. The experiments manipulated imaginability by varying the statistics used to describe negative (e.g. being scarred as a result of laser surgery) and positive (e.g. winning a lottery) low‐probability events. The results strongly supported the frequency format account, whereby imaginability is enhanced through the use of frequency formats for conveying statistical information (e.g. 20 out of 2000 as opposed to 0.01%). However, only limited support was found for exemplar cuing (EC) theory. Overall the results support the claim that the imaginability of outcomes plays a key role in thinking about low‐probability events, but question the mechanisms specified by EC theory for mediating such effects. Copyright © 2007 John Wiley & Sons, Ltd.     

Social discounting and delay discounting

Social discounting was measured as the amount of money a participant was willing to forgo to give a fixed amount (usually $75) to another person. In the first experiment, amount forgone was a hyperbolic function of the social distance between the giver and receiver. In the second experiment, degree of social discounting was an increasing function of reward magnitude whereas degree of delay discounting was a decreasing function of reward magnitude. In the third experiment, the shape of the function relating delayed rewards to equally valued immediate rewards for another person was predicted from individual delay and social discount functions. All in all, the studies show that the social discount function, like delay and probability discount functions, is hyperbolic in form. Copyright © 2007 John Wiley & Sons, Ltd.     

On Reduction Rules,Meaning-as-use,and Proof-theoretic Semantics

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. Presented by Heinrich Wansing     

Horgan on Sleeping Beauty

With the notable exception of David Lewis, most of those writing on the Sleeping Beauty problem have argued that 1/3 is the correct answer. Terence Horgan has provided the clearest account of why, contrary to Lewis, Beauty has evidence against the proposition that the coin comes up heads when she awakens on Monday. In this paper, I argue that Horgan’s proposal fails because it neglects important facts about epistemic probability.     

Synchronic Bayesian updating and the Sleeping Beauty problem: reply to Pust

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4.