Proof Systems for Reasoning about Computation Errors

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents. Presented by Yaroslav Shramko and Heinrich Wansing     

A method for eliciting scale errors in preschool classrooms

Six preschool classrooms, containing children between the ages of 4.0 and 40.0 months, were seeded with miniature items to examine how easily scale errors could be elicited. Observations occurred over a period of 3 months, with a total of 280 min of observations per classroom. A concealed observer documented all interactions with the miniature items. A total of 93 scale errors occurred, with a higher frequency committed by the younger children. These results confirm findings from previous research and suggest that scale errors can be effectively elicited in a preschool classroom. Our approach may provide a useful method for systematically studying the factors that influence scale errors.     

Confidence regions for INDSCAL using the jackknife and bootstrap techniques

Bootstrap and jackknife techniques are used to estimate ellipsoidal confidence regions of group stimulus points derived from INDSCAL. The validity of these estimates is assessed through Monte Carlo analysis. Asymptotic estimates of confidence regions based on a MULTISCALE solution are also evaluated. Our findings suggest that the bootstrap and jackknife techniques may be used to provide statements regarding the accuracy of the relative locations of points in space. Our findings also suggest that MULTISCALE asymptotic estimates of confidence regions based on small samples provide an optimistic view of the actual statistical reliability of the solution. The authors wish to thank Geert DeSoete, Richard A. Harshman, William Heiser, Jon Kettenring, Joseph B. Kruskal, Jacqueline Meulman, James O. Ramsay, John W. Tukey, Paul A. Tukey, and Mike Wish. Sharon L. Weinberg is a consultant at AT&T Bell Laboratories, Murray Hill, New Jersey 07974.     

Stimulus- and response-reinforcer contingencies in autoshaping, operant, classical, and omission training procedures in rats

Separate groups of rats received 500 trials of lever-press training under autoshaping (food delivery followed 10-second lever presentations, or occurred immediately following a response); operant conditioning (responding was necessary for food delivery); and classical conditioning (food followed lever presentations regardless of responding). Each group then received 500 trials on an omission procedure in which food was omitted on trials with a response. Another group received 1000 trials on the omission procedure, and a fifth group, random control, received 1000 uncorrelated presentations of lever and food. The autoshaping, operant, and classical groups reached high response levels by the end of initial training. Acquisition was fastest in the autoshaping group. Responding remained consistently low in the control group. The omission group responded at a level between the control group and the other three groups. During omission training, responding in these three groups declined to the omission-group level. During omission training, the rats continued contacting the lever frequently after lever pressing had declined. Response maintenance under omission training seems not to require topographic similarity between the response and reinforcer-elicited consummatory behaviors.     

Temporal distributions of responding during discrete-trial omission training in rats

Within-session temporal distributions of responding were investigated in three experiments using rats pressing a lever in a discrete-trial omission procedure. This schedule entailed 60, one-minute trials, and a sucrose solution was made available at the end of each trial in which no lever press occurred. In Experiment I, nonnaive rats acquired and maintained responding during this training. Moreover, the probability of a response during any session showed a strong and reliable tendency to increase from the beginning to the end of the session. These results were replicated in Experiment II, using naive animals. In Experiment III, alterations were made in the training procedure, including elimination of response-contingent and noncontingent stimulus changes. Results indicate that stimulus change may be sufficient to maintain low levels of responding whether or not this change is contingent on responding.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Relapse of operant behavior after response elimination with an extinction or an omission contingency

The present study compared relapse after responding was eliminated by extinction or omission training in rats. In Experiment 1, lever pressing was reinforced with food pellets in Context A and then eliminated with either extinction or omission training in Context B. The response was then tested in Contexts A and B in either the presence or absence of free food pellets delivered on a random time schedule. All rats showed higher responding when tested in Context A than Context B, and there was little evidence that omission training attenuated this ABA renewal effect. Noncontingent pellets increased responding after extinction but not after omission. However, when responding on the last day of response elimination was compared to responding during the test in the response-elimination context, there was some evidence that omission-trained rats showed a small increase in responding even when tested with free pellets. Results of Experiment 2 suggest this increase was not due to differences in the temporal distribution of pellets during elimination and the test, and that the result might be due to mere removal of the omission contingency, but any such effect is small and difficult to detect statistically. The results provide new information about factors generating relapse after omission training.