Timeout from concurrent schedules.

Response-contingent timeouts of equal duration and frequency were added to both alternatives of unequal concurrent schedules of reinforcement. For each of 4 pigeons in Experiment 1, relative response rates generally became less extreme as the frequency of timeout increased. In Experiment 2, relative response rates consistently approached indifference as the duration of timeout was increased. Variation in time allocation was less consistent in both experiments. Absolute response rates did not vary with the timeout contingency in either experiment. In a third experiment, neither measure of choice varied systematically when the duration of a postreinforcement blackout was varied. In contrast to the present results, preference has been shown to vary directly with the parameters of shock delivery in related procedures. The pattern of results in the first two experiments follows that obtained with other manipulations of the overall rate of reinforcement in concurrent schedules. The results of the third experiment suggest that an intertrial interval following reinforcement is not a critical feature of the overall rate of reinforcement.     

Positive modal logic

We give a set of postulates for the minimal normal modal logicK ₊ without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are

Spatial metrics of integral and separable dimensions

Two experiments were conducted to investigate the relationship between dimensional integrality and the form of the combination rule or spatial metric used in a similarity judgment task. In Experiment 1, two groups of eight subjects judged the dissimilarity of all pairwise combinations of 12 rectangles differing in height and width (integral dimensions) or 12 circles differing in size and diameter orientation (separable dimensions). The dimensional organization and spatial metric of both sets of dimensions were determined. The results showed that differences in height and width contributed independently to judgments of the overall dissimilarity of rectangles and that these dimensions were combined using a Euclidean metric. In contrast, substantial interactions between circle size and diameter orientation were found. Combinations of these dimensions also appeared to violate the triangle inequality implying that no spatial metric was appropriate. In Experiment 2, parallelogram size and tilt were similarly analyzed. Although some degree of dimensional interaction was observed, it was found that on the average these dimensions were combined using a city-block metric. In a subsequent speeded classification task, orthogonal interference was observed, which suggested that size and tilt are integral dimensions. The implications of both experiments for the supposed association between the Euclidean metric and dimensional integrality are discussed.     

The rapid-smoking technique: Subject characteristics and treatment outcome

There is a lack of consistency in findings regarding subject (S) characteristics and the effects of smoking-control programmes. Research workers appear to assume that abstinence and reduction in smoking rate are merely different points in the same continuum, and therefore seek to correlate S variables with percentage reductions in smoking rate. It is argued that abstinence and reduced smoking are more appropriately viewed as potentially discrete outcomes. Conceptualizing outcome in this manner, a discriminant function analysis was employed to determine whether it is possible to differentiate between Ss who do, or do not, abstain following participation in a treatment programme involving rapid-smoking. It was found that it is possible to discriminate between the two groups of Ss. Advantages deriving from this approach to the investigation of S characteristics and treatment outcome are discussed.     

Deviation from hierarchical structure in recall: Is there an “optimal” structure?

Past research has suggested that proportionally more superordinate than sub-ordinate propositions are recalled from expository texts, following a hierarchical analysis of the text structure. Since free recall has typically followed this hierarchical pattern, several researchers have assumed that the related memory structures are isomorphic to the text structure. However, few of these studies have examined how individual differences and text structure interact to affect free recall. In two experiments, the assumption of hierarchical patterns of children's recall of expository text was tested. In Experiment 1, high- and average-ability fourth graders (9 years old) were asked to read and recall a passage. Experiment 2 was a replication and extension of Experiment 1. In this experiment, fourth and sixth graders (9 and 11 years old) read and recalled a different passage. The combined results of both experiments support the notion that there is probably no one optimal hierarchical structure for storage and retrieval of expository text.     

Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

A theorem in 3-valued model theory with connections to number theory,type theory,and relevant logic

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).