Discrimination training, partial reinforcement, and increases in intertrial interval all reduce response speed in a continuously reinforced key-pecking task

Pigeons were trained in a discrete-trial task in which a response to the center key obtained illumination of a side key and a single response to the side key terminated a trial with either reinforcement or nonreinforcement. Center-key speeds (i.e., reciprocals of latencies) declined with increases in intertrial interval, and it is argued that this effect is related to a decreased likelihood as intertrial interval increases that birds will be near the key at trial onset. Side-key speeds on trials with reinforcement decreased both with increases in intertrial interval and with shifts from continuous reinforcement to either a discrimination or a partial-reinforcement condition. The effects on side-key speeds are compared with effects observed in alley-running tasks using rats, and an interpretation in terms of frustration theory is offered for the results obtained in both types of task.     

The rowwise correlation between two proximity matrices and the partial rowwise correlation

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel'sZ. It is shown that the rowwise matrix correlation coefficient between two matricesX andY is the partial correlation between the entries ofX andY controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.The author wishes to thank the Editor, two referees, Jan van Hooff, and Ruud Derix for their useful comments, and E. J. Dietz for a copy of the algorithm of the Mantel permutation test.     

Range restrictions for product-moment correlation matrices

It is well-known that for a trivariate distribution if two correlations are fixed the remaining one is constrained. Indeed, if one correlation is fixed, then the remaining two are constrained. Both results are extended to the case of a multivariate distribution. The results are applied to some special patterned matrices.     

An evaluation of time-sample measures of behavior

Continuous and time-sample measures of the in-seat behavior of a secretary were obtained. Measurement error, i.e., the extent to which the sample measures deviated from the continuous measure, was a function of the frequency of the sample measurements and the criterion used to score an example of the behavior. If the behavior had to be exhibited throughout the observational interval (whole-interval time sampling), there was a consistent underestimate of the continuous measure. If the behavior had to be exhibited only briefly within the observational interval (partial-interval time sampling), there was a consistent overestimate of the continuous measure. And, if the behavior had to be exhibited at the end of the observational interval (momentary time sampling), overestimations and underestimations of the continuous measure occurred about equally often. As expected, the more frequently the sample measures were made the closer was the agreement between the sample and continuous measures. Two conclusions concerning measurement error in interval time sampling were made. The first was that the error will be a function of the mean time per response. The second is that this error will not be consistent across experimental conditions.     

The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

Taking a closer look: time sampling and measurement error

A person manufactured his in-seat behavior for 15, 30-min sessions so that there were three blocks of five sessions where the behavior occurred 20%, 50%, and 80% of the time. Whole interval, partial interval, and momentary time-sample measures of the behavior were taken and compared to the continuous measure of the behavior i.e., per cent of time the behavior occurred. For interval time sampling, the difference between the continuous and sample measures i.e., measurement error, was: (1) extensive, (2) unidirectional, (3) a function of the time per response, and (4) inconsistent across changes in the continuous measure. A procedural analysis demonstrated that the frequency and duration of behavior are confounded in interval time sampling. Momentary time sampling was found to be superior to interval time sampling in estimating the duration a behavior occurs.     

The Logic of Pragmatic Truth

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.     

A logic of comparative obligation

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in [9], which is formally similar to a fragment of the logic of ability later given in [2], Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of urgency, of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability in [2], provides a complete and decidable system for such a language.     

Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic

We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.     

A note on the factor analysis of partial covariance matrices

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.