Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].     

Nonparametric IRT: Testing the bi-isotonicity of isotonic probabilistic models (ISOP)

Nonparametric tests for testing the validity of polytomous ISOP-models (unidimensional ordinal probabilistic polytomous IRT-models) are presented. Since the ISOP-model is a very general nonparametric unidimensional rating scale model the test statistics apply to a great multitude of latent trait models. A test for the comonotonicity of item sets of two or more items is suggested. Procedures for testing the comonotonicity of two item sets and for item selection are developed. The tests are based on Goodman-Kruskal's gamma index of ordinal association and are generalizations thereof. It is an essential advantage of polytomous ISOP-models within probabilistic IRT-models that the tests of validity of the model can be performed before and without the model being fitted to the data. The new test statistics have the further advantage that no prior order of items or subjects needs to be known.     

Dynamic analyses of mother-child interactions in functional and dysfunctional dyads: a synergetic approach

Describes the application of a new analytical approach (derived from synergetics, a complex dynamic systems theory) to home observational data of mother–child interactions in average dyads and dyads with children referred for disruptive behavior problems at home and school (n = 11 in each group). Results show that (1) the two groups differed in their daily interactions in predictable ways, and (2) the most frequent patterns of interactions observed in the two groups brought them back repeatedly to behave in similar ways toward each other. The findings are in keeping with a body of literature on mother–child interactions. However, they add to it by providing multivariate, graphical representations of these interactions and by offering a conceptual framework within which to move from an observational to an inferential level of analysis. At that level, the transactional processes that are characteristic of functional and dysfunctional relationships may become apparent.     

Predicting face similarity judgements with a computational model of face space

Current models of face representation involve the notion of a high-dimensional face space. Computational models of face space based on principal components analysis (PCA) have been successfully used to predict human judgements of face sex or race. In this work the capability of PCA-based face spaces to predict human judgements of face similarity is examined. Three different paradigms were used. In Experiment 1 subjects learned face-name associations for 18 faces and identified these faces on tachistoscopic presentation. The number of confusions was used as a measure of face similarity. In Experiment 2 the same subjects subjectively rated the similarity of all 153 possible face pairs. In Experiment 3 reaction time to identify a face in an odd-man-out task was measured as an index of face similarity. These empirical measures were correlated with distance of the faces in PCA-based spaces of different dimensionalities. For Experiments 1 and 2 these correlations were highest for one-or two-dimensional face spaces (r=−0.27 vs. −0.28). For Experiment 3 the correlation was highest for a space consisting of 13 dimensions (r=−0.51). Thus PCA-based spaces seem capable to predict human similarity judgements to some extent. Possible reasons for the differences in predictability between paradigms are discussed.     

What the Liar Taught Achilles

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.     

Severe Withdrawal (and Recovery)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals.     

A Systems/Dialectical Model of Supervision: A Symbolic Process

Although there has been a proliferation of models of supervision in the marriage and family therapy literature recently, most tend to focus on methods rather than on the process of supervision. The model presented here is grounded in developmental concepts and focuses on student learning through a dialectical process of cognitive and emotional growth and incorporates three stages: 1) developing relationships; 2) breaking impasses, and 3) orchestrating changes. Students discover that supervision becomes isomorphic with relationship issues that arise in their therapy sessions. Dialectical in nature in that each stage is characterized by the resolution of contradictory emotions, the supervision process helps supervisees experience emotional shifts in their interactions with others, referred to as emotional restructuring.     

Empathic-Cognitive Development in Students of Counseling

Empathy is both crucial to counseling and a desired outcome in higher education. Since the 1960s, many studies have examined the relationship between stages of adult cognitive development and level of empathy, particularly in counselors. Though positive, findings related to this critical research focus have been grounded in small, local samples, leading several investigators to call for a replication using a large, national sample. In response, this study surveyed 340 graduate student members of a large professional counseling association across the United States. Results indicated that more mature forms of thought (according to the Perry scheme) are associated with higher empathy levels (Hogan scale). Implications are drawn for adult development theory, education of counselors, and higher education reform.     

Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢_GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢_PA S^ξ and d(S, G) > 0 imply the inconsistency of PA. This revised version was published online in June 2006 with corrections to the Cover Date.     

Testing a model of codependency for college students in Taiwan based on Bowen's concept of differentiation

The purpose of this study was to test a model of codependency based on Bowen's concept of differentiation for college students in Taiwan. The relations between family‐of‐origin dysfunction, differentiation of self, codependency traits and related symptoms including low self‐esteem, relationship distress and psychological adjustment problems were examined. Data were collected from 567 college students from 2 large, urban universities in northern Taiwan. Results indicated a significantly negative relationship between levels of codependency and self‐differentiation and that self‐differentiation partially mediated the relationship between family‐of‐origin dysfunction and codependency. The implications of these findings for counselling Taiwanese college students who experience codependency traits and related symptoms as well as suggestions for future research are discussed.