Conditionals Right and Left: Probabilities for the Whole Family

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal (in)dependence.     

A Model-Based Approach to Understanding Apraxia in Corticobasal Syndrome

Limb apraxia is a neurological disorder of higher cognitive function characterized by an inability to perform purposeful skilled movements and not attributable to an elementary sensorimotor dysfunction or comprehension difficulty. Corticobasal Syndrome (CBS) is an akinetic rigid syndrome with asymmetric onset and progression with at least one basal ganglia feature (rigidity, limb dystonia or myoclonus) and one cortical feature (limb apraxia, alien hand syndrome or cortical sensory loss). Even though limb apraxia is highly prevalent in CBS (70–80%), very few studies have examined the performance of CBS patients on praxis measures in detail. This review aims to (1) briefly summarize the clinical, neuroanatomical and pathological findings in CBS, (2) briefly outline what limb apraxia is and how it is assessed, (3) to comprehensively review the literature on limb apraxia in CBS to date and (4) to briefly summarize the literature on other forms of apraxia, such as limb-kinetic apraxia and buccofacial apraxia. Overall, the goal of the review is to bring a model-based perspective to the findings available in the literature to date on limb apraxia in CBS.     

A Unified Nonparametric IRT Model for <Emphasis Type="Italic">d</Emphasis>-Dimensional Psychological Test Data (<Emphasis Type="Italic">d</Emphasis>-ISOP)

The (univariate) isotonic psychometric (ISOP) model (Scheiblechner, 1995) is a nonparametric IRT model for dichotomous and polytomous (rating scale) psychological test data. A weak subject independence axiom W1 postulates that the subjects are ordered in the same way except for ties (i.e., similarly or isotonically) by all items of a psychological test. A weak item independence axiom W2 postulates that the order of the items is similar for all subjects. Local independence (LI or W3) is assumed in all models. With these axioms, sample-free unidimensional ordinal measurements of items and subjects become feasible. A cancellation axiom (Co) gives, as a result, the additive isotonic psychometric (ADISOP) model and interval scales for subjects and items, and an independence axiom (W4) gives the completely additive isotonic psychometric (CADISOP) model with an interval scale for the response variable (Scheiblechner, 1999). The d-ISOP, d-ADISOP, and d-CADISOP models are generalizations to d-dimensional dependent variables (e.g., speed and accuracy of response). The author would like to thank an Associate Editor and two anonymous referees and also Professor H.H. Schulze for their very valuable suggestions and corrections.     

Social Influence on Political Judgments: The Case of Presidential Debates

Four experiments investigated the extent to which judgments of candidate performance in presidential debates could be influenced by the mere knowledge of others' reactions. In Experiments 1 and 2 participants watched an intact version of a debate or an edited version in which either "soundbite" one-liners or the audience reaction to those soundbites were removed. In Experiment 3 participants saw what was supposedly the reaction of their fellow participants on screen during the debate. Participants in Experiment 4 were exposed to the reactions of live confederates as they watched the last debate of an active presidential campaign. In all studies, audience reactions produced large shifts in participants' judgments of performance. The results illustrate the power of social context to strongly influence individuals' judgments of even large amounts of relevant, important information, and they support the categorization of presidential debates as ambiguous stimuli, fertile ground for informational social influence.     

Paul Tillich's Perspectives on Ways of Relating Science and Religion

Where do Paul Tillich's views of the relationship between religion and science fit in Ian Barbour's four classifications of conflict, independence, dialogue, and integration? At different levels of analysis, he fits in all of them. In concrete religions and sciences, some conflict is evident, but religion and science can be thought of as having parallel perspectives, languages, and objectives. Tillich's method of correlation itself is a form of dialogue. His theology of nature in “Life and the Spirit” (Part 4 of his Systematic Theology) fits the integration type. His strong “Two Types of Philosophy of Religion” (in Theology of Culture) is a latent natural theology. His system of the sciences is a form of synthesis, a type of integration.     

Correspondence analysis and association models constrained by a conditional independence graph

The manner in which the conditional independence graph of a multiway contingency table effects the fitting and interpretation of the Goodman association model (RC) and of correspondence analysis (CA) is considered.Estimation of the row and column scores is presented in this context by developing a unified framework that includes both models. Incorporation of the conditional independence constraints inherent in the graph may lead to equal or additive scores for the corresponding marginal tables, depending on the topology of the graph. An example of doubly additive scores in the analysis of a Burt subtable is given.Thanks are due to anonymous referees who substantially improved the original draft of this paper.     

Concurrent performances: rate constancies without changeover delays

Pigeons' pecks on two keys were maintained, without changeover delays, by independent variable-interval schedules of food reinforcement. Four regularly cycling 2-min components scheduled reinforcement respectively for both keys, left key only, both keys, and right key only. Initially, reinforcement scheduled for one key alone produced more responding on that key than reinforcement scheduled concurrently for both keys. Continued sessions reduced this difference; response rate on a given key approached constancy, or invariance with respect to the performance on and schedule for the other key. When extinction replaced the reinforcement schedule on either key, responding on that key decreased more during components that scheduled reinforcement for the other key than during those that did not. This demonstration that responses on one key were not supported by reinforcers on the other key suggested that the alternation of concurrent responding and either-key-alone responding prevented concurrent superstitions from developing.     

The effects of concurrent responding and reinforcement on behavioral output

Four birds key pecked on concurrent variable-interval one-minute variable-interval four-minute schedules with a two-second changeover delay. Response rates to the variable-interval one-minute key were then reduced by signaling its reinforcer availability and later by providing its reinforcers independently of responding. Each manipulation increased response rates to the variable-interval four-minute key even though relative reinforcement rates were unchanged. In a final phase, eliminating the variable-interval one-minute key and its schedule produced the highest rates of all to the variable-interval four-minute key. These results show that both reinforcement and response rates to one schedule influence response rates to another schedule. These results join those of Guilkey, Shull, & Brownstein (1975) in failing to replicate Catania (1963). Moreover, they violate the predictions of the equation for simple action (de Villiers & Herrnstein, 1976). In terms of a median-rate measure (reciprocal of the median interresponse time), rates to the variable-interval four-minute key were high when responding was not reduced to the variable-interval one-minute key and were low when it was reduced. This rate difference suggests a process difference between concurrent-schedule procedures that maintain high concurrent response rates versus those that do not. This process difference jeopardizes attempts to integrate single- and concurrent-operant performances within a single formulation.     

The Classification of Propositional Calculi

We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics.     

Comparing Latent Structures of the Grade of Membership,Rasch, and Latent Class Models

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other population parameters fixed, in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The case of a 2 × 2 contingency table is discussed in detail, and a generalization to 2^J tables with J ≥ 3 is sketched. Our approach highlights the main distinction between the GoM model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships. By using the geometric approach we show that, in special cases, the GoM model can be thought of as being similar to an item response theory (IRT) model in representing population heterogeneity. Finally, we show that the GoM item parameters can provide quantities analogous to more general logistic IRT item parameters. As a latent structure model, the GoM model might be considered a useful alternative for a data analysis when both classes of extreme responses, and additional heterogeneity that cannot be captured by those latent classes, are expected in the population. This work was supported by Award #1R03 AG18986-01 from the National Institute on Aging and NIH grant #1R01 CA94212-01. The presentation of the ideas in this paper owes much to discussions with Stephen Fienberg and Brian Junker, Carnegie Mellon University. The author thanks Jim Ramsay and two anonymous reviewers for their valuable comments on earlier drafts of this paper.