Deduction chains for common knowledge

Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system. Given a formula , the deduction chains of are built up by systematically decomposing into its subformulae. In the case where is a valid formula, the decomposition yields a (usually cut-free) proof of . If is not valid, the decomposition produces a countermodel for . In the current paper, we extend this technique to a semiformal system for the Logic of Common Knowledge. The presence of fixed point constructs in this logic leads to potentially infinite-length deduction chains of a non-valid formula, in which case fairness of decomposition requires special attention. An adequate order of decomposition also plays an important role in the reconstruction of the proof of a valid formula from the set of its deduction chains.     

The currency of procurement cost

As the number of instrtumental responses required to procure access to food is increased, animals decrease the frequency of initiating meals and increase meal size, conserving total intake while limiting the increase in the overall cost of feeding. In two studies, one using wheel turns and one using bar presses as the instrumental response, we asked whether freely feeding laboratory rats measure cost according to the energy or the time they expend. In each study we varied both the price (i.e., number of wheel turns or bar presses) and the force required to make a response (i.e., torque on the wheel or weight of the bar). Price affected both procurement time (from the first to the last procurement response) and procurement work, whereas torque and bar weight affected work without altering time in most cases. Meal patterns were altered by all manipulations of price, but changes in torque and bar weight had little effect on meal patterns, except in the conditions in which they altered procurement time. These results suggest that time is a critical currency of procurement cost in rats.     

Barriers to Treatment in an Ethnically Diverse Sample of Families Enrolled in a Community-Based Domestic Violence Intervention

Using quantitative and qualitative data, we examined the association between barriers to treatment, motivating factors, treatment attendance, and outcome in a sample of 63 mothers (most of Asian or Pacific Islander descent) enrolled in a family-based domestic violence treatment program. A high number of perceived barriers was associated with lower attendance and lower scores on assessment of parenting practices at posttreatment. Mothers reported relying on their own motivation, observations of children's improvement, and the quality of their relationships with staff and group members to overcome barriers. A larger number of motivating factors was associated with positive parenting practices at posttreatment. Discussion includes the benefits of a mixed-method approach to measuring barriers and its clinical application to increase treatment participation.     

Holistic processing improves change detection but impairs change identification

It has been just over a century since Gestalt psychologists described the factors that contribute to the holistic processing of visually presented stimuli. Recent research indicates that holistic processing may come at a cost; specifically, the perception of holistic forms may reduce the visibility of constituent parts. In the present experiment, we examined change detection and change identification accuracy with Kanizsa rectangle patterns that were arranged to either form a Gestalt whole or not. Results from an experiment with 62 participants support this trade-off in processing holistic forms. Holistic processing improved the detection of change but obstructed its identification. Results are discussed in terms of both their theoretical significance and their application in areas ranging from baggage screening and the detection of changes in radiological images to the systems that are used to generate composite images of perpetrators on the basis of eyewitness reports.