Association for Behavior Analysis International

In this paper, equations that best describe discounting and risk are presented. Equation 1 addresses the total value of a long sequence of reinforcers. It posits that the total value (molar) of this long sequence of reinforcers is equal to the sum of the values of the individual events in the sequence. This is represented as: A = SAm. The next two difference equations produced simpler equations than differential equations. Equation 2 is a simple difference equation of overall value, A, with respect to time relates overall value. It yields the hyperbolic discounting model of Commons with the sensitivity parameter k1, Woodford and Ducheny (1982), Commons, Woodford and Trudeau (1991), and Mazur (1987). ?V = ?Ai /?ti = ?Ai/(1 + k1di). The second difference Equation 3 is the quantification of Vaughan?s (1976; 1981; Herrnstein & Vaughan, 1980) melioration concept and is also risk (see also, Herrnstein & Prelec, 1991) It is obtained. by taking the difference of Equation 2 and is hyperbolic also, ?(?V)/?di = ?(?Ai /(1 + k2di))/?di. The parameter k2 is an organism?s sensitivity to risk. It is important to note that Equation 3 is also a hyperbolic equation.

Stimulus equivalence is an approach to the study of symbolic behavior from a behavior-analytic approach. In equivalence training, only a small number of relations are trained, after which, numerous relations emerge without specific training (Sidman & Tailby, 1982). Research on conditioned reinforcement has addressed the processes necessary to create conditioned reinforcers (Gollub, 1977). The present study evaluated stimulus equivalence as an operation for producing conditioned reinforcers. Participants were six children, ages 7-10. They were first taught A and B simple discriminations using class-specific consequences, after which, all participants demonstrated three three-member equivalence classes. CD conditional discriminations were then taught using the same class-specific reinforcers, after which, some children showed the emergence of three five-member equivalence classes. The C stimuli were then used as class-specific consequences in E simple discrimination training to test whether, based on class membership with the reinforcing stimuli, the C stimuli would now function as conditioned reinforcers. Thus far, three subjects have shown these emergent relations, expanding the equivalence classes to six members. Two generalization tests were conducted and the reinforcing function of the C stimuli generalized to a novel testing procedure. Results provide evidence for an approach to creating and demonstrating conditioned reinforcers through MTS training and testing procedures. APPROVED

The current study was a systematic continuation of Williams (2016), designed to incorporate an experimental strategy from Sidman et al. (1989). Subjects had mastered simple discrimination training with AB and CD compounds with class-specific reinforcer compounds (CSRC). However, the emergent conditional relations in that study did not meet the formal definitions of the equivalence properties, because the trained baseline relations consisted of simple discriminations only. The current study established relations between an existing member of the classes established in Williams (2016) and a new stimulus; specifically, conditional discriminations DE and DF were trained through differential reinforcement with the same CSRC from Williams (2016). It was of interest to see if training new conditional discriminations provided formal evidence of equivalence, as originally defined. The final phase consisted of simple discrimination probe trials with novel compounds testing for emergent discriminative control in the three-term contingency arrangement. These probes evaluated whether the E and F stimuli functioned similarly to the other members of the class in the originally trained simple discrimination task, even though the stimuli were never presented in simple discrimination training or as part of a training compound. Results spoke to the possibility that functional and equivalence classes are overlapping phenomena.

The interest in stimulus equivalence research has been substantial since Sidmans (1971) documentation of emergent relations. Past experiments have found that, the inclusion of at least one meaningful stimulus in a class of abstract stimuli influences the probability of equivalence class formation. Experiments so far have tested the effect of meaningful stimuli on equivalence class formation by training and testing emergent relations with the inclusion of meaningful stimuli. This study therefore seeks to find out the effect of the inclusion of meaningful stimuli in training but without it in emergent relations testing on equivalence class formation. The study has three experimental conditions: Abstract Group, Picture Group, and No-Picture-in-Test Group. The findings so far show that, one of seven participants formed classes in the Abstract Group, six of seven participants formed classes in the Picture Group, and five of seven participants formed classes in the No-Picture-in-Test Group (See Figure 3). Also, the findings show a significant difference in equivalence class formation between the Abstract Group and the Picture Group, as well as between the Abstract Group and the No-Picture-in Test Group. Furthermore, the findings show no significant difference between the Picture Group, and No-Picture-in Test Group.

Previous studies have shown that behavioral variability can be controlled by environmental contingencies (Page & Neuringer, 1985). Furthermore, some animal studies compared how behavioral variability and stereotyped behavior are resistant to change when using extinction or non-contingent schedule (Arantes et al., 2012). We propose a study to compare resistance to change in behavioral variability and stereotyped behavior in humans. The experiment was divided into training and a perturbation phase. In the first phase, participants are trained to emit either variable or stereotyped letters sequences on a computer. Behavioral variability was operationalized through a lag contingency in which, to be reinforced, the last sequence had to be different from a previous n sequences. Once the criterion of stability was reached, the second phase starts. Perturbation was operationalized using an extinction phase and a non-contingent reinforcement schedule. First results show that behavioral variability is more resistant to change than variable behaviors in extinction phase. There are no significant differences in the non-contingent schedule