Socratic Trees

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction.     

Trees and diagrams of decomposition

We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.     

Trees as memory representations for simple visual patterns

The form of the memory representation for visual patterns consisting of a few line segments was investigated with three tasks. One task was the reproduction of remembered patterns using pencil and paper. The order in which the subparts of those patterns were reproduced was used to make suggestions about possible memory representations for the patterns. The second task involved rating the “goodness” of subparts of the patterns. These ratings were also interpreted as reflecting the underlying representations of the patterns. In the third task, the time required to recognize that a small pattern was part of a larger remembered pattern was used as further evidence about the memory representations of the patterns. The results from all three tasks are consistent with the theory that the memory representations are tree structures. Methods for deriving and comparing tree structures are discussed.     

Trees and Us: Poetic Metaphors and Pastoral Images

This article elaborates on my earlier contention that poetry and pastoral care have a great deal in common (Capps, The Poet’s Gift, 1993) by focusing on Joyce Kilmer’s well-known poem “Trees.” I use this poem to support the metaphorical association of trees and human beings and to advocate for the pastoral image of the upholder. A brief sketch of Kilmer’s life is presented, and parodies of the poem are used to address the question whether pens are mightier than swords (a question that Kilmer’s own life as a poet and soldier also evokes). The article concludes with Denise Levertov’s poem “From Below” which, together with Kilmer’s “Trees,” illumines the image of the pastor as ordained to be the upholder of the community and of the individuals who comprise it.     

制止尊树为"仙"的迷信行为

《燕赵都市报》3月1日报道,在河北省邯郸县南堡乡小北堡村老邯郸——大名公路的西侧路旁,一棵高大的杨树成了人们朝拜的对象,人们在树上还筑起了“杨仙庙”。1994年春天,杨树上面由于虫害等原因造成的杨絮结团,个别人传为“杨仙显灵”,使许多人上当受骗。在大名县县城南关一条老街上长着一棵高大的槐树,树冠直径达20余米,树干直径约1米有余,虽然部分枝干已     

Characterizing linguistic structure with mutual information

We explore mutual information (MI) as a means of characterizing linguistic statistical structure. The MI between two linguistic tokens x and y is the degree to which seeing x helps us anticipate the occurrence of y. We computed MI between words in 595 samples of written text in 25 languages. Our analyses indicate that MI dependencies do not extend beyond a range of five words. Moreover, the similarity between MI profiles of different languages was used to cluster the languages. These results are discussed in terms of a putative link between short‐term memory and linguistic structure and the further utility of MI in terms of characterizing the latter.     

Best linear composites with a specified structure

Least squares linear composites of predictors for estimating several criteria are derived, satisfying the restriction that the composites have an arbitrary specified intercorrelation matrix. These composites are compared with the usual unrestricted regression composites. An illustrative example is provided. The derivation depends on a general result, given in an appendix, about best-fitting orthonormal transformations.This research was done while the author was a Fellow at The Center for Advanced Study in the Behavioral Sciences. The investigation was supported by a Public Health Service fellowship, 1 F3 MH-28, 495-01 (PS), from the National Institute of Mental Health. Preparation of the paper was supported in part by Grant MH 07722 from the National Institute of Mental Health, Public Health Service, for work done at Carnegie-Mellon University.     

Perception of Glass pattern structure with stereopsis

Stereograms are presented which demonstrate that the perceptual salience of structure in Glass patterns may be destroyed or created by the introduction of stereoscopic depth effects. Novel three-dimensional pattern structures can also be produced. Proposals concerning the nature of the primal sketch are evaluated in the light of these findings, and it is concluded that the findings are consistent with the view that depth derived from disparity information is explicitly represented in the primal sketch.     

Temporal structure coding with and without awareness

In order to interpret a constantly changing environment, visual events far apart in space and time must be integrated into a unified percept. While spatial properties of invisible signals are known to be encoded without awareness, the fate of temporal properties remains largely unknown. Here, we probed temporal integration for two distinct motion stimuli that were either visible or rendered invisible using continuous flash suppression. We found that when invisible, both the direction of apparent motion and the gender of point-light walkers were processed only when defined across short time periods (i.e., respectively 100 ms and 1000 ms). This limitation was not observed under full visibility. These similar findings at two different hierarchical levels of processing suggest that temporal integration windows shrink in the absence of perceptual awareness. We discuss this phenomenon as a key prediction of the global neuronal workspace and the information integration theories of consciousness.     

Investigating stereotype structure with empirical network models

In this work we present empirical network models as a new approach in the investigation of stereotype structure. We will argue that empirical network models can provide more insight into stereotype structure because they do not suffer from the inherent constraints of factor analysis and multidimensional scaling (e.g., group features interpreted homogeneously only on the basis of their shared variance, impossibility to adequately represent cognitive schemas, difficulties to make inferences on the basis of dimensions potentially overlapping). In the present research we show how empirical network models can represent stereotypes as dynamic cognitive structures clustered in different substructures. These structures will be based on both the stereotype content and the co-occurrence of features in each group target. Additionally, this research shows how using empirical networks can contribute to broadening the interpretation of stereotypes representing them in the framework of prejudice or intergroup attitudes.