Dissertations / Theses on the topic 'Equivalence relation'

A well-researched line showing equivalence performances in a wide variety of areas has been conducted in the field of Behavior Analysis (BA). One area demonstrates that relating relations is a behavioral account of analogical thinking. Relating relations may have implications for the development of analogical training given that analogical reasoning is seen as the foundation of intelligence yet research in this area is limited. A protocol by Stewart, Barnes-Holmes, and Weil (2009) was developed to train children in analogical reasoning using equivalence-equivalence relations. The purpose of this study was to evaluate an equivalence-equivalence training protocol based on Stewart et al. (2009) and test whether the protocol was effective in training equivalence-equivalence responding to 7 and 8-year-old children. A secondary purpose was to test whether training in equivalence-equivalence responding increased performances on analogical tests. All five participants were dismissed throughout the study. Participant 1 was dismissed during the pre-assessments and all other participants were dismissed during intervention. Because none of the participants passed the equivalence-equivalence training, increases in performance in analogical testes were not analyzed. Individual performance data from training are examined and analyzed to provide an account of the failures to pass the equivalence-equivalence protocol.

We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.

Prouver l’équivalence de programmes écrits dans un langage fonctionnel avec références est un problème notoirement difficile. L’objectif de cette thèse est de proposer un système logique dans lequel de telles preuves peuvent être formalisées, et dans certains cas inférées automatiquement. Dans la première partie, une méthode générique d’extension de la théorie des types dépendants est proposée, basée sur une interprétation du forcing vu comme une traduction de préfaisceaux de la théorie des types. Cette extension dote la théorie des types de constructions récursives gardées, qui sont utilisées ensuite pour raisonner sur les références d’ordre supérieure. Dans une deuxième partie, nous définissons une sémantique des jeux nominale opérationnelle pour un langage avec références d’ordre supérieur. Elle marie la structure catégorique de la sémantique des jeux avec une représentation sous forme de traces de la dénotation des programmes, qui se calcule de manière opérationnelle et dispose donc de bonnes propriétés de modularité. Cette sémantique nous permet ensuite de prouver la complétude de relations logiques à la Kripke définit de manière directe, via l’utilisation de types récursifs gardés, sans utilisation de la biorthogonalité. Une telle définition directe nécessite l’utilisation de mondes omniscient et un contrôle fin des locations divulguées. Finalement, nous introduisons une logique temporelle qui donne un cadre pour définir ces relations logiques à la Kripke. Nous ramenons alors le problème de l’équivalence contextuelle à la satisfiabilité d’une formule de cette logique générée automatique, c’est à dire à l’existence d’un monde validant cette formule. Sous certaines conditions, cette satisfiabilité peut être décidée via l’utilisation d’un solveur SMT. La complétude de notre méthode devrait permettre d’obtenir des résultats de décidabilité pour l’équivalence contextuelle de certains fragment du langage considéré, en fournissant un algorithme pour construire de tels mondes<br>Proving program equivalence for a functional language with references is a notoriously difficult problem. The goal of this thesis is to propose a logical system in which such proofs can be formalized, and in some cases inferred automatically. In the first part, a generic extension method of dependent type theory is proposed, based on a forcing interpretation seen as a presheaf translation of type theory. This extension equips type theory with guarded recursive constructions, which are subsequently used to reason on higher-order references. In the second part, we define a nominal game semantics for a language with higher-order references. It marries the categorical structure of game semantics with a trace representation of denotations of programs, which can be computed operationally and thus have good modularity properties. Using this semantics, we can prove the completeness of Kripke logical relations defined in a direct way, using guarded recursive types, without using biorthogonality. Such a direct definition requires omniscient worlds and a fine control of disclosed locations. Finally, we introduce a temporal logic which gives a framework to define these Kripke logical relations. The problem of contextual equivalence is then reduced to the satisfiability of an automatically generated formula defined in this logic, i.e. to the existence of a world validating this formula. Under some conditions, this satisfiability can be decided using a SMT solver. Completeness of our methods opens the possibility of getting decidability results of contextual equivalence for some fragments of the language, by giving an algorithm to build such worlds

The purpose of this study was to examine the relation between stimulus equivalence (briefly, networks of relations among stimuli) and the extension of stimulus function (briefly, spread of effect across network) more closely than has been possible before. The traditional view of this relation suggests that equivalence classes mediate the extension of stimulus function and are, therefore, necessary for any extension to occur. This study used a preparation in which the conditional discriminations required for the development of equivalence classes and the simple discriminations required for the extension of function were trained or tested simultaneously. Results suggest that equivalence are not necessary for the extension of stimulus function though they may be sufficient.

The experiment was an attempt to gain a more precise understanding of the temporal relation between the development of analytic units and equivalence relations. Two prompting procedures were used during training to pinpoint when eight subjects learned the conditional discriminations. Near simultaneous presentation of probe and training trials allowed for examination of the temporal relation between conditional discrimination acquisition and derived performances on stimulus equivalence probes. The data show that, for seven of eight subjects, a decreased reliance on prompts was coincident with the development of equivalence-consistent choices on either all or some probe trials, which suggests that the development of analytic units is sufficient to give rise to equivalence relations among stimuli.

This thesis proposes a generalisation of pre-logical predicates to simply typed formal systems and their categorical models. We analyse the three elements involved in pre-logical predicates -- syntax, semantics and predicates -- within a categorical framework for typed binding syntax and semantics. We then formulate generalised pre-logical predicates and show two distinguishing properties: a) equivalence with the basic lemma and b) closure of binary pre-logical relations under relational composition. To test the adequacy of this generalisation, we derive pre-logical predicates for various calculi and their categorical models including variations of lambda calculi and non-lambda calculi such as many-sorted algebras as well as first-order logic. We then apply generalised pre-logical predicates to characterising behavioural equivalence. Examples of constructive data refinement of typed formal systems are shown, where behavioural equivalence plays a crucial role in achieving data abstraction.

The main goal of this work is to determine values of elastic constants of orthotropic, transversely isotropic and cubic materials through indentation tests on thin layers bonded to rigid substrates. Accordingly, we first use the Stroh formalism to provide an analytical solution for generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and indented by a rigid cylindrical indenter. The mixed boundary-value problem is challenging since the deformed indented surface of the layer contacting the rigid cylinder is unknown a priori, and is to be determined as a part of the solution of the problem. For a rigid parabolic prismatic indenter contacting either an isotropic layer or an orthotropic layer, the computed solution is found to compare well with solutions available in the literature. Parametric studies have been conducted to delimit the length and the thickness of the layer for which the derived relation between the axial load and the indentation depth is valid. We then derive an expression relating the axial load, the indentation depth, and the elastic constants of an orthotropic material. This relation is specialized to a cubic material (e.g., an FCC single crystal). By using results of three virtual (i.e., numerical) indentation tests on the same specimen oriented differently, we compute values of the elastic moduli, and show that they agree well with their expected values. The technique can be extended to other anisotropic materials. We review the literature on relations between deformations at the atomic level and stresses and strains defined at the continuum level. These are then used to compare stress and strain distributions in mechanical tests performed on atomic systems and their equivalent continuum structures. Whereas averaged stresses and strains defined in terms of the overall deformations of the atomic system match well with those derived from the continuum description of the body, their local spatial distributions differ.<br>Ph. D.

Robotic motion planning aspires to match the ease and efficiency with which humans move through and interact with their environment. Yet state of the art robotic planners fall short of human abilities; they are slower in computation, and the results are often of lower quality. One stumbling block in traditional motion planning is that points and paths are often considered in isolation. Many planners fail to recognize that substantial shared information exists among path alternatives. Exploitation of the geometric and topological relationships among path alternatives can therefore lead to increased efficiency and competency. These benefits include: better-informed path sampling, dramatically faster collision checking, and a deeper understanding of the trade-offs in path selection. In path sampling, the principle of locality is introduced as a basis for constructing an adaptive, probabilistic, geometric model to influence the selection of paths for collision test. Recognizing that collision testing consumes a sizable majority of planning time and that only collision-free paths provide value in selecting a path to execute on the robot, this model provides a significant increase in efficiency by circumventing collision testing paths that can be predicted to collide with obstacles. In the area of collision testing, an equivalence relation termed local path equivalence, is employed to discover when the work of testing a path has been previously performed. The swept volumes of adjoining path alternatives frequently overlap, implying that a continuum of intermediate paths exists as well. By recognizing such neighboring paths with related shapes and outcomes, up to 90% of paths may be tested implicitly in experiments, bypassing the traditional, expensive collision test and delivering a net 300% boost in collision test performance. Local path equivalence may also be applied to the path selection problem in order to recognize higher-level navigation options and make smarter choices. This thesis presents theoretical and experimental results in each of these three areas, as well as inspiration on the connections to how humans reason about moving through spaces.

This thesis investigates the sensitivity of derived monetary valuations of the well-being effects of non-market goods, by considering, in turn, the four components that contribute to these calculations. Comparisons are made to the current subjective well-being (SWB) literature by altering one component at a time in a willingness to pay (WTP) function, in addition to varying the estimator used when calculating WTP. The first component varied is the measure of income used; a more robust, up-to-date measure is proposed that takes into account household size, economies of scale and composition, plus other improvements over current income scaling approaches including equivalence scales. Secondly, anticipation and adaptation effects are examined, in order to allow for the dynamics of SWB in WTP valuations. Thirdly, due to the ordered nature of the dependent variable, the effects of both cardinal and ordinal models on WTP derivations are investigated. Such models include the ordered logit fixed effects (FE) model (see for example Das and Van Soest (1999), Ferrer-i-Carbonell and Frijters (2004) and Baetschmann et al. (2011)). The final input to be varied is whether income endogeneity is accounted for. A control function approach is used in this case. A key finding is that all four inputs in the WTP calculation contribute significantly to the estimated WTP values. However, the degree to which each input influences the variation in WTP values differs substantially. The three main contributing factors to WTP variations are the income variable chosen, anticipation and adaptation effects, and controlling for endogeneity. Additionally, this thesis proposes a new way to define WTP that is also valid for ordered estimators. Whilst the standard WTP approach relies simply on coefficient ratios at a point in time, the method proposed here uses the finding that statistically significant anticipation and adaptation effects, along with adaptation to all non-market events (except for unemployment) suggest that there are concerns with taking WTP values as yearly valuations that assume constant effects on SWB. By instead defining WTP as the summation of the value of all WTP effects over all lag and lead effect periods, the total value of an event can be calculated. This definition presents further weaknesses of the original method by showing that because of significant lag and lead effects for events such as divorce and widowhood, these events have substantially larger WTP values than first thought. This leads to the major finding in this study that rank orders are not preserved when controlling for income endogeneity, even when comparing two model specifications that are identical in all other respects. Therefore, despite absolute WTP valuations appearing more similar for linear and ordered estimators when a more appropriate model specification is in place, the rank orders are affected. This finding argues against papers such as Powdthavee and van den Berg (2011) that find that rank orders are preserved for WTP valuations when modelling SWB. In conclusion, given rank orders are generally not preserved when a small change is made in the model specification, the validity of the WTP method is significantly reduced. Finally, the above methodology is applied to education, with the main contribution to the education literature being that the positive effects on SWB from education only exist in terms of lead effects.

On considère R une relation d'équivalence borélienne standard de type I I1 sur un espace de probabilités (X, µ). On étudie une certaine propriété d'homogénéité pour un graphage fixé de la relation R : on suppose que les feuilles du graphage sont toutes isomorphes à un certain graphe transitif (connexe, infini, localement fini) Γ. Que peut-on dire sur la relation ? Dans ce cas, en considérant une action "à la Mackey", on montre qu'il existe (Z ,η) un revêtement standard probabilisé de (X, µ), une action libre (qui préserve η) sur Z du groupe G (localement compact, à base dénombrable d'ouverts) des automorphismes du graphe et un isomorphisme stable des groupoïdes mesurés associés. On fait le lien entre les propriétés du groupe G et celles de la relation de départ ; en particulier la propriété (T), (H) et la moyennabilité "passent" du graphe à la relation et réciproquement. On déduit aussi de la construction quelques couplages d'équivalence mesurée (ou plus généralement des "randembeddings") entre certains sous-groupes des automorphismes de Γ et tout groupe qui contient orbitalement la relation R. Dans un deuxième chapitre, on aborde le cas particulier de la propriété (T) relative pour les paires de groupes (ΓxZ^2, Z^2), où Γ est un sous-groupe non moyennable de SL(2,Z). Cette propriété a d'abord été prouvée par Marc Burger, puis "re-démontrée" plus "visuellement" quelques années plus tard dans le cas de SL(2,Z)xZ^2 par Y. Shalom, en utilisant des découpages du plan. On reprend cette technique dans le cas général du théorème de Burger afin d'obtenir par un algorithme des constantes de Kazhdan explicites pour toute paire (ΓxZ^2, Z^2).

Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Il Capitolo 1 focalizza l’attenzione sulla relazione tra tempo libero relazionale e soddisfazione di vita dichiarata. Nella letteratura empirica sul benessere soggettivo, è generalmente riconosciuto che il tempo libero dedicato ad interazioni sociali è correlato positivamente con la soddisfazione di vita riportata per mezzo di interviste. L’analisi tenta di definire se l’associazione tra le due variabili sia di tipo causale. A questo scopo viene condotta un’analisi empirica sul German Socio Economic Panel (GSOEP) 1984 - 2007. La disponibilità di osservazioni individuali ripetute nel tempo consente l’uso di un modello lineare ad effetti fissi che corregge per le variabili omesse persistenti nel tempo, come i tratti della personalità di un individuo. Il modello non corregge però per variabili omesse mutabili nel tempo. Si ricorre quindi ad una stima strumentata del tempo dedicato alle attività sociali. La tecnica di strumentazione si basa sulla variazione del tempo relazionale a seguito del pensionamento. Dato che lo status di pensionamento individuale ha un’influenza diretta sul livello di benessere soggettivo, la variabile strumentale adottata è la proporzione di persone in pensione per anno e per macro regione tedesca (Germania Est/Ovest). Nella regressione del primo stadio si evidenzia come l'impatto della proporzione di pensionati sul tempo devoluto alle attività sociali sia significativamente differente tra donne e uomini. Sfruttando tale eterogeneità, siamo in grado di strumentare con successo la variabile di interesse. L’analisi riesce dunque a dimostrare che il tempo libero dedicato alle interazioni sociali ha un effetto causale positivo sulla soddisfazione di vita. L’evidenza empirica di tale nesso di causalità può avere importanti implicazioni sulle politiche sociali. Il Capitolo 2 affronta il tema della soddisfazione di vita riportata dagli immigrati e dell’impatto delle relazioni diplomatiche tra il paese d’origine e d’approdo. L’analisi tenta quindi di stimare il valore di buone relazioni bilaterali. L’analisi utilizza un indice che misura il grado di cooperazione e conflitto nei rapporti tra Stati. L’indice è stato ideato da studiosi di Relazioni Internazionali per l’analisi quantitativa degli eventi internazionali. Esso è costruito come somma di eventi occorsi tra Stati, pesati in base al grado di cooperazione/conflitto attribuito da un panel di esperti. Nella nostra analisi, l’indice d’intensità delle relazioni bilaterali è associato agli immigrati intervistati nel GSOEP. L’indice ha una variabilità sia temporale che tra individui. Ciò permette di condurre un’analisi econometrica che sfrutta i vantaggi di un dataset longitudinale controllando per gli effetti fissi individuali. L’analisi empirica porta ad affermare che buone relazioni bilaterali sono significativamente correlate con la soddisfazione di vita degli immigrati, specialmente nel caso di eventi frequenti. Tale correlazione è maggiormente rilevante per gli immigrati che si trovando da più tempo in Germania e che hanno intenzione di rimanervi. Questo risultato conferma quanto già affermato in letteratura, ossia, che le relazioni tra Stati influenzano direttamente la qualità di vita degli immigrati nel paese di destinazione, ma non depongono a favore del processo d’integrazione. Usando, infine, il calcolo della variazione compensativa applicata all’indice delle relazioni tra Stati se ne monetarizza l’effetto. In conclusione, l’analisi giunge ad attribuire un valore significativo alla diplomazia: buone relazioni tra il paese d’origine e di destinazione hanno importanti esternalità positive per coloro che abitano all’estero. Il Capitolo 3 si incentra, invece, sulla relazione, fin qui poco esplorata, tra soddisfazione di vita e figli. Nella fiorente letteratura empirica sulle determinanti della soddisfazione di vita si tiene conto del numero di bambini presenti nell’unità famigliare tra le variabile esplicative standard assieme al reddito familiare disponibile (spesso non corretto per la dimensione familiare). L’impatto sulla soddisfazione di vita di tale variabile risulta associare sia il beneficio di un effetto relazionale sia il costo in termini monetari e di tempo dei figli. Nella letteratura sulla soddisfazione di vita si trova, infatti, che il coefficiente per i figli non è significativo, o è addirittura negativo. Nel lavoro qui presentato si cerca di discriminare l’effetto monetario dei figli da quello non monetario, attraverso l’utilizzo delle comuni scale di equivalenza per il reddito familiare. L’analisi empirica da noi condotta è basata su cittadini tedeschi intervistati dal GSOEP negli anni 1984 - 2007. Si dimostra, dunque, che, adottando delle elasticità di scale sempre maggiori, ossia assumendo minime, se non nulle, economie di scala nella formazione del nucleo familiare, l’impatto del numero di bambini sulla soddisfazione di vita divenga positivo. Viene anche rifiutata l’ipotesi di omogeneità dei coefficienti date le notevoli differenze nell’impatto dei figli conviventi sull’individuo a seconda del genere e della località geografica d’origine (Germania Est/Ovest). Si conclude che l’effetto non pecuniario dei figli sia maggiore per gli uomini, gli individui con un reddito familiare inferiore o uguale alla mediana, e soprattutto per i cittadini dell’Est. I risultati ottenuti nei sottogruppi possono essere imputati, secondo la nostra interpretazione a differenti costi opportunità e norme socio-culturali.<br>Chapter 1 focuses on the relation between social leisure and subjective well-being. In the empirical literature it is generally found that social leisure is positively correlated with life satisfaction. We ask if this association captures a genuine causal effect of the consumption of a social leisure time index on subjective well-being by using panel data from the German Socio Economic Panel (GSOEP) 1984 - 2007. The availability of multiple observations per individual allows us to use the fixed effect estimation technique which takes care of time invariant personal traits and omitted variables. This strategy of estimation solves only a part of the endogeneity issues which bias our coefficient for social leisure. We then adopt an Instrumental-Variables estimation. Our identification strategy exploits the change in social leisure brought about by retirement. However, individual retirement directly influences subjective well-being. Therefore, we instrument social leisure with the ratio of retired people in the sample by year and geographic location. Our results show a gendered difference in the impact of this ratio on social life. Exploiting the gender heterogeneity brings us to a successful instrumentation of social leisure. We can therefore conclude that social leisure has a positive causal effect on life satisfaction. Chapter 2 addresses the issue of subjective well-being of migrants and diplomatic relation. In particular, the paper represents an attempt to establish the value of good relationships between countries by considering their effects on a group of individuals who are arguably intimately affected by them: immigrants. We appeal to an index of conflict/cooperation constructed by experts in International Relations Sciences and currently used to carry out quantitative analysis on events data. Such index is an annual weighted sum of news items occurring between countries according to their content of conflict and cooperation, as established by a panel of experts in the field. This index is matched to a sample of immigrants in Germany who belong to the GSOEP data. The index of bilateral relations thus exhibits both time-series and cross-section variation and allows us to use a linear fixed effect estimation method. We find that good relations are positively and significantly correlated with immigrant life satisfaction, especially when we downplay low-value news events. This significant effect is much stronger for immigrants who have been in Germany longer, and who expect to stay there forever. This is consistent with good relations directly affecting the quality of immigrants’ lives in the host country, but is not consistent with assimilation. In order to evaluate the economic significance of our finding we finally compute the compensating surplus of the index of international relations. There is thus a significant value to diplomacy: good relationships between home and host countries generate significant well-being externalities for those who live abroad. Chapter 3 addresses the issue not enough explored by the happiness literature of the relation between children and life satisfaction. Indeed, the empirical analyses on the determinants of life satisfaction often include the number of children living in the household in the standard set of socio demographic explanatory variables together with household disposable income (often not corrected for household size). In this way, the estimation of the children’s coefficient does not fully discriminate between the monetary and non-monetary impact of children in the household. In our paper, we compare results obtained by correcting income for different equivalence scales. Indeed, equivalence scales are intended to measure the variation in income needed to bring households of different compositions to the same welfare level. The main arguments revolve around economies of scale in household formation. Our empirical analysis is based on the West and East subsamples of the GSOEP 1984 – 2007. We find that when economies of scale are assumed to be perfects (i.e. the household size and composition does not reduce the fruition of available income) children living in the household affect negatively the life satisfaction of adults. Adopting less perfect economies of scale in the household brings the children’s coefficient to shift from negative to positive and significant. We further reject slope homogeneity as we find strong differences between gender and regions of the impact of children living in the household. We show that the positive “non pecuniary” effect of children is stronger for men, below or equal to median income households and, most of all, for East Germans. We interpret these subsample split results as driven by heterogeneous opportunity costs and cultural traits.

Nous proposons une nouvelle methodologie de simulation symbolique, permettant la verification des circuits sequentiels decrits a des niveaux d'abstraction differents. Nous avons utilise un outil automatique de verification formelle afin de montrer l'equivalence entre une description structurelle precisant les details de realisation et sa specification comportementale. Des descriptions au niveau portes logiques issues d'un outil de synthese commercial ont ete comparees a des specifications comportementales et structurelles au niveau transfert de registres. Cependant, il n'est pas necessaire que la specification soit synthetisable ni qu'elle soit equivalente a la realisation a chaque cycle d'horloge. Ulterieurement cette methode pourra aussi s'appliquer a la verification des proprietes. La simulation symbolique est executee en suivant des chemins dont l'outil garantit la coherence logique. Nous obtenons un bon compromis entre precision et vitesse en detectant des equivalences grace a un ensemble extensible de techniques. Nous utilisons des diagrammes de decisions binaires (obdd) pour detecter les equivalences dans certains cas particuliers. Nous evitons l'explosion combinatoire en utilisant les resultats des autres techniques de detection et en ne representant qu'une petite partie du probleme a verifier par des diagrammes de decisions. La cooperation de toutes les techniques, et la generation de traces permettant la correction d'erreurs, ont ete rendues possibles par le fait que nous associons des relations a des classes d'equivalence, au lieu de manipuler des expressions symboliques.

Due to changing age demographics in the United States, by 2050, an estimated 62.1 Americans will be over the age of 65 and the number of Americans with cognitive impairment, such as Alzheimer’s disease, will increase drastically as well (Alzheimer’s Association, 2014; Ortman, Velkoff, & Hogan, 2014). Once a diagnosis or behavioral indicators of cognitive impairment are present, it would be beneficial to apply a treatment package that promotes the maintenance or re-establishment of stimulus control in the environment. From a behavioral perspective, stimulus control aids in learning and memory through both respondent and operant conditioning. In the current study, stimulus equivalence training was completed and compared to cognitive and functional assessments scores with older adult participants with and without cognitive impairment as a systematic replication of Gallagher and Keenan (2009). Formation of equivalence relations after exposure to linear series (LS) training with 2 3-member stimulus classes across arbitrary, familiar, and stimuli from Gallagher and Keenan (2009) was compared via trials to criterion, accuracy per relation, and session length to scores on the Mini-Mental Status Exam (MMSE), Saint Louis University State Exam (SLUMS), and Barthel ADL Index. Several methodological changes were applied to a second study to examine the impact of increased programmed stimuli, training changes, and the use of one-to-many (OTM) and many-to-one (MTO) training structures with 3 3-member stimulus classes on equivalence formation. Composite performance scores were created for accuracy during LS, OTM, and MTO training. Non-parametric analyses were conducted between assessment and composite scores. The SLUMS and Barthel ADL Index were not correlated with any composite scores. However, MMSE scores and LS composite scores were correlated. The SLUMS was more sensitive to the detection of cognitive impairment as judged by classification and diagnoses. OTM and MTO composite scores also had a strong, positive correlation. Overall, more participants demonstrated higher levels of accurate responding during LS training than during OTM and MTO training. In contrast to previous research, only 25% of the sample demonstrated equivalence formation. Limitations and future research directions are discussed.

AN ABSTRACT OF THE THESIS OF Hailey Williams, for the Master’s Degree in Behavior Analysis, presented on 7/8/16, at Southern Illinois University Carbondale. TITLE: TEACHING EQUIVALENCE RELATIONS THROUGH DRAWING USING THE PEAK-E CURRICULUM MAJOR PROFESSOR: Dr. Mark R. Dixon The purpose of this study was to observe the formation of equivalence response classes using drawing to demonstrate the transformation of stimulus function from arbitrary textual words to simple drawings. Two children with Autism were taught directly trained relations, which paired together three stimuli from three separate class formations. The children were taught to relate A-B and B-C relations in trial blocks, and then tested with B-A and C-A relations. This train-test method was used to see if derived relations had emerged. Both participants demonstrated adequate learning in achieve mastery criteria in all the directly trained and derived relations from this study. The data is represented in a multiple baseline graph with an embedded multiple probe design. The outcome of this study indicates that the use of drawing and other creative behaviors have value in both relation frame theory and PEAK. There are also several implications of the study addressed here, including drawing as a verbal behavior and the role of internal events and covert behaviors in learning.

The study of Borel equivalence relations on Polish spaces has become a major area of focus within descriptive set theory. Primarily, work in this area has been carried out using the standard methods of descriptive set theory. In this work, however, we develop a model-theoretic framework suitable for the study of Borel equivalence relations, introducing a class of objects we call Borel structurings. We then use these structurings to examine conditions under which marker sets for Borel equivalence relations can be concluded to exist or not exist, as well as investigating to what extent the Compactness Theorem from first-order logic continues to hold for Borel structurings.

The experimenter asked if documented equivalence class membership would influence the development of shared discriminative stimulus function established through simple successive discrimination training. In Experiment 1, equivalence classes were established with two sets of 9 stimuli. Common stimulus functions were then trained within or across the equivalence classes. Greater acquisition rates of the simple discriminations with stimuli drawn from within the equivalence classes were observed. In Experiment 2, a third stimulus set was added with which no equivalence relations were explicitly trained. The findings of Experiment 1 were replicated, but the Set 3 results were inconsistent across subjects. The outcomes of the two experiments demonstrate that equivalence classes have an effect on other behavioral relations which requires further investigation.

Language development involves the learning of multiple sets of equivalence relations. Research has shown that if certain conditional relations are directly taught for one member of a class of stimuli, then additional conditional relations often emerge for other members of that class, without direct training. There are currently very few studies which have demonstrated this research finding in individuals with autism spectrum disorder (ASD). The research design used for the present experiment was a single-subject AB cross-over design replicated across five plus five children with ASD and five plus five typically developing children. The children with ASD and the typically developing children were matched on their level of vocabulary development. Participants were randomly assigned to either a teaching order Treatment A+B or a teaching order Treatment B+A. The first experimental treatment (Treatment A+B) involved teaching responses to S1 and S2 in the order Condition A followed by Condition B. The second experimental treatment (Treatment B+A) involved teaching responses to S1 and S2 in the order Condition B followed by Condition A. Condition A involved the teaching of AB and AC (hear-select) relations, and Condition B involved the teaching of BA and CA (see-say) relations. The participants in this study were taught stimulus-response relations that involved six names and numerical representations of quantities in the range 1 to 18. Tests for the emergence of symmetry and transitivity were then conducted. The relationships between the emergence of the untaught equivalence relations and teaching condition, the entering characteristics of the children, and trials to criterion were examined. The results of this study showed that five out of ten participants with ASD demonstrated the emergence of all of the untaught equivalence relations regardless of the treatment condition. The remaining five participants with ASD showed substantial variability. Of the children in the Typically Developing Group nine of the ten demonstrated emergence of all of the untaught equivalence relations. The variables that were most strongly correlated with the emergence of untaught equivalence relations were speed of acquisition of taught relations, functional academics scores, and the chronological age of the participants. The effect of communication ability, pre-academic numeracy skill level, and the experimental treatment (the teaching order conditions) were not strongly related to the emergence of untaught equivalence relations. These findings suggest that outcomes on tests for emergence may have been a function of children’s rate of development and prior learning history. The findings of the current study are best explained by Relational Frame Theory. The implications of these findings for teaching children with ASD and other developmental disabilities, and also teaching in general are discussed.

<p>This study describes the English verb ’consider’ and the characteristics of some of its senses. An investigation of this kind may be useful, since a machine translation program, SYSTRAN, has invariably translated ’consider’ with the Swedish verbs ’betrakta’ (Eng: ’view’, regard’) and ’anse’ (Eng: ’regard’). This handling of ’consider’ is not satisfactory in all contexts.</p><p>Since ’consider’ is a cogitative verb, it is fascinating to observe that both the theory of semantic primes and universals and conceptual semantics are concerned with cogitation in various ways. Anna Wierzbicka, who is one of the advocates of semantic primes and universals, argues that THINK should be considered as a semantic prime. Moreover, one of the prime issues of conceptual semantics is to describe how thoughts are constructed by virtue of e.g. linguistic components, perception and experience.</p><p>In order to define and clarify the distinctions between the different senses, we have taken advantage of the theory of mental spaces.</p><p>This thesis has been structured in accordance with the meanings that have been indicated in WordNet as to ’consider’. As a consequence, the senses that ’consider’ represents have been organized to form the subsequent groups: ’Observation’, ’Opinion’ together with its sub-group ’Likelihood’ and ’Cogitation’ followed by its sub-group ’Attention/Consideration’.</p><p>A concordance tool, http://www.nla.se/culler, provided us with 90 literary quotations that were collected in a corpus. Afterwards, these citations were distributed between the groups mentioned above and translated into Swedish by SYSTRAN.</p><p>Furthermore, the meanings as to ’consider’ have also been related to the senses, recorded by the FrameNet scholars. Here, ’consider’ is regarded as a verb of ’Cogitation’ and ’Categorization’.</p><p>When this study was accomplished, it could be inferred that certain senses are connected to specific syntactic constructions. In other cases, however, the distinctions between various meanings can only be explained by virtue of semantics.</p><p>To conclude, it appears to be likely that an implementation is facilitated if a specific syntactic construction can be tied to a particular sense. This may be the case concerning some meanings of ’consider’. Machine translation is presumably a much more laborious task, if one is solely governed by semantic conditions.</p>

We present an axiomatization of relational varieties, i.e., classes of relational structures closed under formation of products and retracts, by a certain class of first-order sentences. We apply this result to categorically equivalent algebras and primal algebras. We consider the relational varieties generated by structures with minimal clone, rigid structures and two-element structures.

Sidman and Tailby (1982) established procedures to analyze the nature of stimulus to stimulus relations established by conditional discriminations. Their research describes specific behavioral tests to determine the establishment of properties that define the relations of equivalence. An equivalence relation requires the demonstration of three conditional relations: reflexivity, symmetry, and transitivity. The equivalence stimulus paradigm provides a method to account for novel responding. The research suggests that equivalence relations provide a more efficient and effective approach to the assessment, analysis, and instruction of skills. The present research examined the effectiveness of the formation of an equivalence class in teaching young children coin value relations. The second aspect of the study was to determine if there was a relationship between equivalence class formation and generalization of the skills established to other settings. Five children, 4- and 5-years old, were selected to participate in the study based on their lack of skills in the area of coin values and purchasing an item with dimes or quarters equaling fifth cents. The experimental task was presented on a Macintosh computer with HyperCard programming. The experimental stimuli consisted of pictures of dimes, quarters, and Hershey candy bars presented in match-to-sample procedures. Two conditional discriminations were taught (if A then B and if B then C.). The formation of an equivalence class was evaluated by if C then A. Generalization across settings was tested after the formation of an equivalence class by having the children purchase a Hershey candy bar with dimes at a play store. A multiple baseline experimentaldesign was used to demonstrate a functional relationship between the formation of an equivalence class and generalization of skills across settings. The present research provides supportive evidence that coin value relations can be taught to young children using equivalence procedures. The study also demonstrated generalization of novel, untaught stimuli across settings, after the formation of an equivalence class. A posttest on generalization across settings was conducted 3 months after the study. Long-term stability of equivalence relations was demonstrated by three of the subjects.<br>Department of Special Education

This study evaluates the efficacy of using Equivalence Based Instruction (EBI) to teach historical figures to teenagers with autism in a group setting. Stimuli consisted of three eight-member classes of (A) vocal names of inventors, (B) pictures of inventors, and (C) textual names of their inventions. Participants were assigned their own directly trained class members (Participant 1- A₁₂₃₄, B₁₂₃₄ ,C₁₂₃₄) and (Participant 2 - A₅₆₇₈, B₅₆₇₈, C₅₆₇₈). Participants trained on relation A→B, then after mastery, trained on relation B→C. Probes were conducted followed both A→B and B→C training to assess mastery. Participants each received instructions for three trials then alternated as observer for three trials. Results found both participants demonstrated class formation on their trained stimuli, and one participant demonstrated class formation for his train and observed stimuli. This suggest observational learning with EBI was effective for teaching new academic skills to teenagers with autism.

The present investigation examined observational learning during equivalence-based instruction using the PEAK Equivalence curriculum, across five children with disabilities. A multiple baseline across skills was used to evaluate observational learning across the participants, including directly observed relations, as well as derived symmetrical and transitive relations. Each skill contained 5 stimulus classes, where a subset of relations for a single class was trained for each participant. The remaining 4 class subsets were observed by each of the participants. For the derived relations, participants never observed peers contact reinforcement for correct responding nor did they themselves contact reinforcement for correct responding. After multiple sessions, results indicated increases in both observed directly trained relations, as well as emergent derived relations. Over the course of the sessions, the participants average correct answers increased from an average of 12% during baseline to100% at the end of the training phase and during a follow-up test probe. The results have implications for equivalence-based ABA instruction in schools and other settings where group-based instruction is common in application with individuals with disabilities.

Fluent component performances may be more readily available for recombination into more complex repertoires. This experiment considered the stimulus equivalence preparation as a laboratory analog for the co-adduction said to occur in generative instruction. Seven adults received minimum training on 18 conditional discriminations, components of 9 potential stimulus equivalence classes. Training was interrupted periodically with tests to determine whether fluency of original relations predicted emergence of derived relations. Fluency predicted emergence in 2 of 17 instances of emergent derived relations for 4 subjects. One subject demonstrated fluency without derived relations. Training accuracies as low as 58% preceded emergence for 3 subjects. Fluency appears to be neither necessary nor sufficient for derived relations. Fluency's role may be in retention and complex application tasks rather than acquisition of behavioral relations.

In recent years, there has been an increasing interest in the study of human operant behavior. One area of study reflecting this interest is the study of the formation of equivalent classes of stimuli by human subjects. The focus of the present research was the study of the conditions under which classes of equivalent stimuli can be inferred to be under conditional control. In Experiment 1-A, three college students were trained to respond to a balanced five-term contingency via a visual-visual simultaneous matching-to-sample task with two choices of comparison stimuli. Probe tests showed that subjects' behavior could be described as being controlled by positive and negative stimulus relations. When the second-order stimulus was removed during subsequent probes, none of the three subjects demonstrated strong correct responses to the four-term unit relations. Also, none of the three subjects demonstrated the expected transitive relations when the second-order (five-term) stimulus was removed. In Experiment 1-B--with the same three subjects--explicit training of the four-term unit relations showed the expected transitive relations in the absence of the second-order stimulus. In Experiments 2 through 5--using a matching-to-sample task similar to that used in Experiments 1-A and 1-B--five subjects were trained to respond to comparison stimuli C and E in the presence of sample A and second-order stimulus X and to comparison stimuli Band Fin the presence of sample D and second-order stimulus X. Likewise, the subjects were trained to respond to comparison stimuli Band Fin the presence of sample A and second-order stimulus Y and to comparison stimuli C and E in the presence of sample D and second-order stimulus Y. Probe tests for transitive relations showed that four of the five subjects eventually demonstrated four three-member classes of equivalent stimuli that functioned separately under the control of the second-order stimuli. The four subjects demonstrating the classes of equivalent stimuli either a) demonstrated the transitive relations immediately orb) demonstrated the transitive relations after explict retraining of the underlying four-term unit relations. The results of all experiments together indicated that the composition of classes of equivalent stimuli can be conditionally controlled by either a) removing the second-order stimulus orb) training subjects to respond to classes of equivalent stimuli under the control of other explicit visual second-order stimuli. The results are discussed in terms of verbal behavior, emergent behavior, and conceptual development.

The present study evaluated the use of stimulus equivalence to train novel money relations with adults with developmental disabilities. Three programs from the PEAK Relational Training System: Equivalence Module (PEAK-E) were used: Reflexivity: Money, Symmetry: Money to Monetary Value and Equivalence: Monetary Exchange. The overall goal of the study was to evaluate how stimulus equivalence could help the subjects improve money skills, a socially significant behavior for all adults. The study used a multiple probe design across programs to evaluate skill acquisition following the train/test procedure for each program. Results demonstrated a significant increase in PEAK scores from baseline probes for two of the three programs for all subjects. Additionally, results showed that all subjects learned untrained skills. The results of this study demonstrated the value of stimulus equivalence for teaching money skills as well the efficacy of the PEAK-E training system to teach adults with developmental disabilities.

Autism is a neurological disorder which impairs the individual's social interactions and communication. Such impairments lead to deficits in learning which accumulate over time. Finding effective and efficient technologies to teach children with autism helps to minimize deficits and teach children new skills to be independent learners. There is previous research on technologies such as discrete trail training (DTT), antecedent based interventions, and consequence based interventions which have to be shown to be effective, however, more research is needed to find more cost effective and efficient procedures.. The PEAK Stimulus Equivalence Training Module seeks to teach children with Autism in a concise easy to follow manual. Past research has shown stimulus equivalence to not only effectively teach children with autism novel skills, but also has shown the emergence of untrained relations. The present study uses the PEAK module with three boys with autism, between the ages of 6 and 8, to teach novel stimuli including, planets, holidays, and sports teams and to test for the emergence of untrained relations. Results showed that the all participants demonstrated derived relations. Implications for future research are discussed.

Equivalence relations are criteria for comparing the behavior of systems. They have important applications in the verification and testing of communications protocols. This thesis presents our investigation on equivalence relations in two parts. Part One contains mainly the theoretical results. It first gives a survey on many important equivalence relations. It then proposes new types of reachability for indeterministic distributed systems and a unified definition which reveals the essential and common features of many equivalence relations. This uniform approach points out that the various equivalence relations differ from one another mainly in the domain of the action sequences, the types of reachability and the observable properties of the reached sets of states. Exhibited behavior equivalence relation is redefined and a new polynomial time algorithm for its verification is presented. Three reduction methods among the equivalence relations are discussed and a number of results on property-preserved transformations are given. A proof that EB equivalence is stronger than testing equivalence in non-strongly convergent labeled transition systems is presented. A disproof of the conclusion existing in literature that EB equivalence is stronger than weak equivalence is provided. Part Two reports our implementation of the various verification algorithms in a system call LTS-EVS in the Sun Workstation.

<p>This experiment tested the effectiveness of an equivalence-based instructional procedure on verb acquisition among five typically developing, low-performing first grade students. Additionally, the researcher compared the possibly differential effects of picture and video formats to teach actions as concepts. The researcher custom-designed a computerized, multiple exemplar plus fluency-based match-to-sample training procedure to directly train 96 total relations across 24 potential generalized equivalence classes (i.e., 24 verbs). After training, students completed post-tests for 408 potential untaught relations per verb. The independent variables in this study were the instructional procedure implemented and the two instructional visual depiction formats&mdash;photo and video. A multiple treatments, multi-probe experimental design was conducted. The researcher measured (1) accuracy, (2) rate of response, (3) the number of criterion-level performances, (4) the number of derived and generalized relations, and (5) the number of stimulus classes formed across three dependent variables: emergent relations tests, generalized emergence tests, and retention tests. The results showed that (1) the procedure implemented was overall effective in facilitating verb acquisition across some but not all measures tested; (2) video format was as, if not more, effective compared to picture format; and (3) which format promotes relatively better acquisition depends on the unique learning history of the individual student. This was a preliminary investigation and, therefore, provides initial information on verb acquisition, adds to the literature in generalized equivalence class formation, and serves as a basis for many areas of additional research. </p>

A persistent challenge for behaviorally-based accounts of learning has been providing an account of learning that occurs in the absence of systematically programmed contingencies of reinforcement. Symmetry, one type of emergent behavior, has been repeatedly demonstrated with humans, but has been considerably more difficult to demonstrate with non-humans. In this study, pigeons were exposed to a go/no-go procedure in which hue stimuli were presented full screen on a touchscreen monitor. Pigeons learned 12 baseline relations in less than 30 days. Traditional measures used to evaluate symmetry indicated that, during tests, three of the four birds responded more to the reverse of relations that were reinforced in training than to the reverse of relations that were not reinforced in training. However, additional analyses of these data suggests that these differences were driven by one of two trial types and that symmetry was only observed for one of the two predicted relations. These data systematically replicate and extend work by Urcuioli and colleagues and point to areas where further research is needed.

This thesis examines three questions concerned with the relative income needs of families of different sizes - often summarised by indices known as ???equivalence scales???. The first is the extent to which researchers and policy makers should offset the costs of family composition (eg the expenditure costs of children) with the benefits associated with demographic choice (eg the ???joys of parenthood???). Chapter 2 concludes that there are demographic and financial market constraints that will often make a narrow focus on expenditure costs appropriate for distributional research and tax/transfer policies. However, this will not always be the case. One implication of this result is that it may be reasonable for distributional research to use different equivalence scales for adults and children in the same household. Part 2 of the thesis introduces a new method for the estimation of the within-household income distribution and expenditure costs of different family types. This is based upon the household welfare model of Samuelson together with Lau???s method for modelling the joint consumption of household goods. In Chapter 4, this method is applied to the estimation of equivalence scales for older singles and married couples. The estimation is based upon a detailed set of assumptions about the extent of joint consumption for 17 different commodity groups. The main conclusions are that: the theoretical model fits the observed behaviour well (with the exception of some home production effects); that aged couples share their income relatively evenly; and that the relative rate of pension for aged singles in Australia is probably too low. In Part 3, the thesis examines how changes in poverty can be estimated when there is uncertainty about the equivalence scale. The thesis proposes a new method which permits a set of upper and lower bounds for the equivalence scale to be assumed, which in turn determine upper and lower bounds for the increase in poverty. This method is applied to measure the change in poverty in Australia during the 1980s. Equivalence scales can be found that imply either an increase or a decrease in poverty.

O objetivo desta dissertação é apresentar a construção dos números reais a partir de cortes de Dedekind. Para isso, vamos estudar os números naturais, os números inteiros, os números racionais e as propriedades envolvidas. Então, a partir dos números racionais, iremos construir o corpo dos números reais e estabelecer suas propriedades. Um corte de Dedekind, assim nomeado em homenagem ao matemático alemão Richard Dedekind, é uma partição dos números racionais em dois conjuntos não vazios A e B em que cada elemento de A é menor do que todos os elementos de B e A não contém um elemento máximo. Se B contiver um elemento mínimo, então o corte representará este elemento mínimo, que é um número racional. Se B não contiver um elemento mínimo, então o corte definirá um único número irracional, que preenche o espaço entre A e B. Desta forma, pode-se construir o conjunto dos números reais a partir dos racionais e estabelecer suas propriedades. Esta dissertação proporcionará aos estudantes do Ensino Médio, interessados em Matemática, uma formação sólida em um de seus pilares, que é o conjunto dos números reais e suas operações algébricas e propriedades. Isso será muito importante para a formação destes alunos e sua atuação educacional.<br>The purpose of this dissertation is to present the construction of the real numbers from Dedekind cuts. For this, we study the natural numbers, the integers, the rational numbers and some properties involved. Then, based on the rational numbers, we construct the field of the real numbers and establish their properties. A Dedekind cut, named after the German mathematician Richard Dedekind, is a partition of the rational numbers into two non-empty sets A and B, such that each element of A is smaller than all elements of B and A does not contain a maximum element. If B contains a minimum element, then the cut represents this minimum element, which is a rational number. If B does not contain a minimal element, then the cut defines a single irrational number, which \"fills the gap\" between A and B. In this way, one can construct the set of real numbers from the rationals and establish their properties. This dissertation provides students who like Mathematics a solid basis in one of the pillars of Mathematics, which is the set of real numbers and their algebraic operations and properties. This text will be very important for your educational background and performance.

Made available in DSpace on 2016-04-29T13:17:33Z (GMT). No. of bitstreams: 1 Diana Ferroni Bast.pdf: 725034 bytes, checksum: adb63192e443e561b81d67f59e0cd649 (MD5) Previous issue date: 2010-10-15<br>This experiment examined the conditioned emotional functions after a experimental condition on the formation of stimulus equivalence relations. This study was composed by four phases and it has been initiated after six participants have completed the IDATE and BDI scales. Three favorite words had been chosen by participants in the first phase and they would be used at the end of experiment. The second phase consisted on the formation of stimulus equivalence of arbitrary stimuli and all participants have achieved the 90% criterion. After, Phase 3 was designed to stablish an operant response function for 3 stimuli of the previous phase that would acquire distincts functions: neutral, aversive (S-) and positive reinforcing stimuli (S+). Three participants showed conditioned suppression when submitted to the S-. Finally, in the Phase 4, new stimulus equivalence relations would be done with each stimuli used in the Phase 2 and new stimuli (arabic and positive words that had been choosen by participants). The results showed that, two participants could not reach the last criterion for the formation of stimulus equivalence relations and they required more testing trials in the MTS training blocks-to-criterion and equivalence testing for S-/S+ condition and S+/S+. These two participants were found in the group that demonstrated conditioned supperssion on Phase 3. The others participants required less repetitions and it was detected different patterns of mistake among them, probably related with the experimental history of Phase 3. The fact of the participants scored anxiety or depression in the scales utilized was not correlated with the main interfering effect but experimental history was. Implications of this study for treatment of clinical treatments are considered<br>O presente estudo investigou a emergência de relações entre estímulos que adquiriram funções diferentes a partir de uma história experimental. O estudo foi composto por quatro fases e iniciado após os seis participantes terem preenchido escalas para ansiedade e depressão, IDATE e BDI. A primeira fase consistia na escolha de três palavras favoritas que iriam ser utilizadas no final do estudo. Na segunda fase, os participantes foram expostos a um procedimento que permitiu a emergência da equivalência de estímulos fisicamente diferentes até atingirem o critério de 90% em testes de equivalência. Na terceira fase, foi construída uma história experimental na qual três estímulos que faziam parte da fase anterior adquiririam distintas funções como estímulo aversivo, reforçador e neutro. Três participantes demonstraram supressão condicionada perante a apresentação do estímulo aversivo condicionado. Finalmente, na última fase, os participantes foram submetidos a um procedimento que estabelecia novas relações arbitrárias de equivalência com todos os estímulos utilizados na Fase 2 e novos estímulos (sinais árabes e as palavras escolhidas pelos participantes na 1ª Fase). Apenas dois participantes não conseguiram estabelecer relações de equivalência e erraram em grande quantidade ao relacionar estímulos funcionalmente diferentes aversivo-reforçador e funcionalmente semelhantes reforçador-reforçador . Esses dois participantes encontravam-se entre aqueles que demonstraram supressão condicionada perante S- na Fase 3. Os demais participantes necessitaram fazer poucas repetições durante o treino de simetria e foram detectados distintos padrões de erros entre eles, o que provavelmente teve relação com a história experimental construída na Fase 3. O fato dos participantes terem apresentado escores para depressão ou ansiedade não foi correlacionado com os resultados, mas a história experimental demonstrou uma possível correlação. Implicações dos resultados deste estudo para o tratamento clínico da ansiedade foram considerados

This study sought to evaluate the efficiency of the methods outlined in the Promoting the Emergence of Advanced Knowledge Relational Training System Equivalence Module (PEAK-E) utilizing a single-subject design. Three participants from a Midwest town were recruited to participate in the study and were assessed and validity, reliability, and efficacy were evaluated to determine the assessments ability to identify three language skills that weren’t currently present in their repertoire. Baseline levels determined that the 3 skills for each participant (a total of 9 skills across the 3 participants) were not currently present in their repertoire prior to implementation of PEAK-E programs, as the participants demonstrated low levels of correct responding. Upon completion of program implementation across all three participants with autism, mastery criteria was obtained for all directly trained skills, and relations were derived for 9 out of 9 programs.

Relational Density Theory describes quantifiable higher-order properties governing relational framing of verbal organisms. Consistent with Newtonian classical mechanics, the theory posits that relational networks, and relating itself, will demonstrate the higher-order emergent properties of density, volume, and mass. Thus, networks that contain more relations (volume) that are stronger (density) will be more resistant to change (i.e., contain greater mass; mass = volume * density). Consistent with Newton’s law of gravity, networks that contain greater mass will also demonstrate force, accelerating the acquisition of new relations beyond that accounted for by direct acting contingencies, therefore demonstrating emergent self-organization that is highly susceptible to small changes at initial conditions. The current set of experiments provides initial proof of concept data for foundational principles introduced in the theory. Experiment 1 (N = 6) models the volumetric mass density formula, predicting that networks with greater volume and density will be more resistant to change (i.e., contain greater mass) when counterconditioning is applied to a subset of derived relations contained within experimentally established networks. Results were consistent with theoretical predictions based on density on 10 of 12 occasions, and resistance appeared greater for relations operating at greater volume. Experiment 2 (N = 6) extended directly from Experiment 1, generating a density differential through exposure at initial training conditions, and utilizing response time as a measure of relational density. Results again demonstrated successful prediction of resistance corresponding with the emergent density differential on 10 of 12 occasions, along with overall greater resistance corresponding with and volumetric increases. Experiment 3 (N = 9) demonstrated that relational volume can detract from relational density when accurate responding is near 100%, and that network density is predictive of class mergers when no merged responding is ever reinforced, suggesting that network mass can exert force on relational responding in the absence of any experimental conditioning (i.e., gravity). Taken together, results have radical implications for understanding the self-emergent nature of complex human behavior, with applications in therapy and treatment, as well as in understanding the human condition more broadly.