Relating Equivalence Relations to Equivalence Relations: A Relational Framing Model of Complex Human Functioning

The concept of parallel equivalence operator arises from the equivalence operator and the pansystems series-parallel model, by which a family of arbitrary binary relations can be converted into equivalence relations. This paper presents the pansystems rough set based on parallel equivalence operator, which provides a new thought to process rough sets with non-equivalence relations(incomplete, uncertain, or vague information), as well as makes the rough set theory more practical in applications.

In 1982, Pawlak proposed the concept of rough sets with practical purpose of representing indiscernibility of elements. Even it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in the real-world application. Here, coverings of, or non-equivalence relations on, the universe can be considered to represent a more realistic model instead of partition in which a generalized model of rough sets was proposed. In this paper, based on α-coverings of the universe, a generalized concept of rough membership functions is proposed and defined into three values, minimum, maximum and average. Their properties are examined.KeywordsSimilarity ClassRealistic ViewGranular ComputingConditional SymmetryFuzzy Binary RelationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Two experiments investigated possible interactions between existing equivalence relations among stimuli and the acquisition of simple discriminations involving the same stimuli. During the first phase of Experiment 1, two adult humans learned two sets of six conditional relations among arbitrary visual stimuli designed to produce two independent sets of three, three-member equivalence classes (Set 1 and Set 2). Subjects whose performance met accuracy criteria on tests for equivalence relations proceeded to a second phase in which subjects were taught, via reinforcement, to make the same response to a cluster of three stimuli (e.g., response 1 in the presence of A1, B1, and C1). The clusters of three stimuli were initially consistent with documented equivalence relations for both Set 1 and Set 2 stimuli. In the second half of this phase, the contingencies were realigned such that the simple discriminations being established were consistent with documented equivalence relations for Set 1 stimuli but inconsistent for Set 2 stimuli. Results showed that the simple discriminations were acquired faster for Set 1 stimuli than for Set 2 stimuli. Experiment 2 introduced a third set of stimuli as a control set and systematically replicated Experiment 1 with four subjects. This study found that three of four subjects acquired simple discriminations faster when the cluster of stimuli were drawn from within equivalence classes rather than across equivalence classes. The development of equivalence relations with Set 3 stimuli constrained the utility of the control condition in this experiment. The results are best interpreted as suggesting that existing equivalence relations among stimuli can interact with the development of analytic units such as simple discriminations to either facilitate or retard their development.

Although the literature on reinforcement in behavioral psychology is extensive, few studies have examined the derived transformation of reinforcing functions in accordance with equivalence classes, and no published research has yet examined the derived transformation of consequential functions in accordance with nonequivalence relations. In the present study, which consisted of four experiments, the basic preparation was as follows. First, an arbitrary stimulus, B2, was established as a conditioned punisher, using direct stimulus pairing. Following nonarbitrary relational training, designed to establish SAME and OPPOSITE contextual cues, subjects were exposed to arbitrary relational training using these contextual cues to establish A1 as the same as B1 and C1, and as opposite to B2 and C2. Subsequently, C2 (based on its Same relation with B2) functioned as a punisher and C1 (based on its Opposite relation with B2) functioned as a reinforcer in a simultaneous discrimination task. Critically, the C1 stimulus acquired reinforcing functions, based on the derived relation of Opposite, although no such function had actually been established for any member of the network. Furthermore, these effects were observed across ABA reversals in the baseline contingencies.

Recent research has demonstrated the transfer of induced mood functions through equivalence relations by means of a musical mood-induction procedure. The research described in this article replicated and extended such work, primarily with the inclusion of a baseline and two types of reversal procedures. First, 16 adult participants were trained and tested for the formation of two three-member equivalence classes (A1-B1-C1 and A2-B2-C2). A musical mood-induction procedure was used to induce happy and sad mood states in the presence of the B stimuli, and a transfer of mood functions test was administered to determine whether the corresponding mood functions had transferred via equivalence to the C stimuli. Participants were then exposed to either Reversal 1, in which only the functions attached to the B stimuli were reversed, or to Reversal 2, in which the structure of the equivalence classes was altered. At all stages throughout the experiment, participants were asked to rate their current mood state by using mood and incentive rating scales. The findings of the current study replicated the results of previous research in demonstrating a clear transfer of mood functions via equivalence relations. This outcome is compared with the existing literature about mood induction and the transfer of mood functions.

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.

The most complex human functions — which are the most difficult to quantify — are also the most vulnerable to trauma. As the severity of injury increases, so does the likelihood that basic functional activities will also be disrupted. In addition, psychological disorders hamper the individual’s ability to develop methods to compensate for functional, vocational and interpersonal skills deficits. Central to the individual’s problems is the inability to adapt to novel circumstances. The brain-injured individual may be unable to determine what is interfering with his functioning and as a result be unable to change his behaviour to improve performance. This chapter describes some of the psychological deficits which may affect individuals after brain injury. An attempt is made to relate the more abstract description of deficits to the patient’s actual difficulties in functional activities. This chapter discusses the psychological sequelae of brain injury under the headings of arousal and attention, perception, memory and information processing, language and problem solving. Although these functions are described separately, it should be remembered that the human brain is an integrated unit and division by cognitive function is only on a conceptual level (Stuss and Benson, 1987).

Spatial reasoning, where novel spatial relationships are inferred based on trained relationships, can be conceptualized as arbitrarily applicable spatial relational responding. Here, we conducted two experiments to develop and validate, for the first time, a laboratory procedure to establish arbitrarily applicable spatial relational responding in adult humans. In Experiment 1, participants were trained on nonarbitrary spatial relational tasks designed to establish contextual cues for left of, right of, above, and below. Contextual cues were then used to train a series of arbitrary spatial relations involving four abstract shapes. Following training in a subset of arbitrary relations (A is left of B, B is above C, C is right of D), subsequent testing examined the emergence of untrained spatial relations (B is right of A, C is below B, D is left of C, D is below A and A is above D). When absent in initial tests, spatial relational responding was facilitated by a remedial training procedure incorporating nonarbitrary relational guidance. Participants showed patterns of spatial relational responding consistent with test relations. In Experiment 2, a variant reversal design yielded predictable, reversed spatial relational responses. Overall, the present procedures represent the first empirical demonstration of arbitrarily applicable spatial relational responding and thus, arguably, the first functional analytic model of spatial reasoning.

To simulate the emotional judging function seen in some clinical problems, matching-to-sample training was used to establish three-member stimulus equivalence classes consisting of abstract paintings. Pictures with strongly positive or negative emotional content were then paired with only one of the paintings in each class, and transfer of the judgement function to the other stimuli in the equivalence class was tested. A single-case, multi-element pretest-posttest design was used with 10 participants in each of two experiments. Stimulus equivalence emerged in all participants, with 95%-100% correct responses. However, transfer of the judgement rating function appeared consistently in only three participants in Experiment 1. In Experiment 2, transfer test trials were done only in the posttest phase to obviate the effects of pre-experimental history, preference or memory, but only two participants consistently showed transfer. We conclude that the experimental method we used controls for procedural variables that might account for the between-participant and within-stimulus variability usually found in earlier transfer experiments. In contrast to the appearance of stimulus equivalence, the emergence of transfer of function did not appear to be an automatic process.

The flexible control of sequential behavior is a fundamental aspect of speech, enabling endless reordering of a limited set of learned vocal elements (syllables or words). Songbirds are phylogenetically distant from humans but share both the capacity for vocal learning and neural circuitry for vocal control that includes direct pallial-brainstem projections. Based on these similarities, we hypothesized that songbirds might likewise be able to learn flexible, moment-by-moment control over vocalizations. Here, we demonstrate that Bengalese finches (Lonchura striata domestica), which sing variable syllable sequences, can learn to rapidly modify the probability of specific sequences (e.g. ‘ab-c’ versus ‘ab-d’) in response to arbitrary visual cues. Moreover, once learned, this modulation of sequencing occurs immediately following changes in contextual cues and persists without external reinforcement. Our findings reveal a capacity in songbirds for learned contextual control over syllable sequencing that parallels human cognitive control over syllable sequencing in speech.

For tight oil reservoirs, because of ultra-low permeability, the radial flow is difficult to be obtained in pressure build-up testing which results in multi-solution of flow model and interpretation results. How to determine the right model and identify the right interpretation result are the key questions. This paper presents a well test interpretation methodology based on time and space scales to increase accuracy of well-test interpretation results. Two steps are performed to determine reasonable flow model and interpretation results based on time and space scales. For the time scales, the history of well testing data for a single well are interpreted and the interpretation results are compared first. Then for space scales, the well test data in space for multi-wells are analyzed. At this stage, the interpretation results of adjacent wells are compared. The reservoir geological data and the production history are used as a reference to appraise the well test interpretation results. After these two steps, the reasonable interpretation model and interpretation results can be determined. Two cases selected from Changqing oilfields whose permeabilities are almost under 0.5mD and fluid flow rates are very low are analyzed and the great application effect is attained. This methodology is applied in Changqing oilfields extensively and is proved to be a great methodology in ultra-low permeability oil reservoirs. It can be expanded to other unconventional reservoirs, such as tight gas, shale gas and so on. The innovation is that this paper derives a well testing analysis methodology to determine right model and identify the right interpretation result based on time and space scales. It can decrease the errors which are caused by multi-solution of flow model and many interpretation results.

The mechanisms underlying the transition from acute to chronic pain are unclear but may involve the persistence or strengthening of pain memories acquired in part through associative learning. Contextual cues, which comprise the environment in which events occur, were recently described as a critical regulator of pain memory; both male rodents and humans exhibit increased pain sensitivity in environments recently associated with a single painful experience. It is unknown, however, how repeated exposure to an acute painful unconditioned stimulus in a distinct context modifies pain sensitivity or the expectation of pain in that environment. To answer this question, we conditioned mice to associate distinct contexts with either repeated administration of a mild visceral pain stimulus (intraperitoneal injection of acetic acid) or vehicle injection over the course of 3 days. On the final day of experiments, animals received either an acid injection or vehicle injection prior to being placed into both contexts. In this way, contextual control of pain sensitivity and pain expectation could be tested respectively. When re-exposed to the noxious stimulus in a familiar environment, both male and female mice exhibited context-dependent conditioned analgesia, a phenomenon mediated by endogenous opioid signaling. However, when expecting the presentation of a painful stimulus in a given context, males exhibited conditioned hypersensitivity whereas females exhibited endogenous opioid-mediated conditioned analgesia. These results are evidence that pain perception and engagement of endogenous opioid systems can be modified through their psychological association with environmental cues. Successful determination of the brain circuits involved in this sexually dimorphic anticipatory response may allow for the manipulation of pain memories, which may contribute to the development of chronic pain states.

The control exerted by contextual cues over classically conditioned responding was assessed for rats with electrolytic lesions of the dorsal hippocampus and sham-operated controls. In 3 experiments the rats received initial training with 2 reinforced cues, each presented in its own distinctive context, followed by a nonreinforced test in which the cues were presented in the other context. Both control and operated subjects showed context specificity, as evidenced by less vigorous responding to these cues than to cues presented on test in their original contexts. The groups did not differ in their ability to learn an explicit discrimination in which a given cue was reinforced in one context and nonreinforced in a different context (although the groups did differ on a simple autoshaping task). It is concluded that a special role for the hippocampus in the contextual control of conditioned responding still remains to be demonstrated.

There is much debate as to the extent and nature of functional specialization within the different subregions of the prefrontal cortex. The current study was undertaken to investigate the effect of damage to medial prefrontal cortex subregions in the rat. Rats were trained on two biconditional discrimination tasks, one auditory and one visual, in two different contexts. At test, they received presentations of audiovisual compounds of these training stimuli in extinction. These compounds had dictated either the same (congruent trials) or different (incongruent trials) responses during training. In sham-operated controls, contextual cues came to control responding to conflicting information provided by incongruent stimulus compounds. Experiment 1 demonstrated that this contextual control of responding was not evident in individual rats with large amounts of damage that included the prelimbic and cingulate subregions of the prefrontal cortex. Experiment 2 further dissociated the result of Experiment 1, demonstrating that lesions specific to the anterior cingulate cortex were sufficient to produce a deficit early on during presentation of an incongruent stimulus compound but that performance was unimpaired as presentation progressed. This early deficit suggests a role for the anterior cingulate cortex in the detection of response conflict, and for the medial prefrontal cortex in the contextual control of competing responses, providing evidence for functional specialization within the rat prefrontal cortex.

Contextual control is a key component of behavioral accounts of complex human behavior. Relational contextual cues afford such contextual control, and are routinely established and employed in experimental analyses of relational responding (i.e., responding to one stimulus based on its relationship with another stimulus). Surprisingly, the functional properties of relational contextual cues have not yet been subjected to systematic experimental analysis. Across several pairs of experiments, we investigated these properties, and in each case compared them to the properties of discriminative stimuli because comparisons with a more well studied stimulus property would be informative. Experiment 1 assessed the sensitivity to counterconditioning and reductions in the contingency between cue occurrence and response opportunity. Experiment 2 assessed the impact of three fixed ratio schedules on the acquisition of the function of relational contextual cue. Experiment 3 investigated the impact of higher-order contextual control. Results indicated that relational contextual cues and discriminative stimuli are equally sensitive to counterconditioning, the reinforcement contingency strength, and higher-order contextual control. These results shed new light on the functional properties of relational contextual cues, which has implications for researchers and practitioners designing protocols to establish patterns of relational responding.