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Counterfactual thoughts involve the consideration of how events might have progressed differently. These conditional statements include an antecedent (e.g., "If only I were less impulsive") and a consequent (e.g., "I would not have been unfaithful") (Markman, Gavanski, Sherman, & McMullen, 1993). The statements allow an alternate ending to what actually occurred and they often occur spontaneously. Such statements have many variations and may evoke negative (e.g., Regret that my relationship might be over) and positive (e.g., Hope that I am learning from my mistakes) reactions.This study investigated the relationship between other-generated counterfactual statements and the recipient's emotional response to these statements. Vignettes were developed by the author and distributed to a college student population. The content of the vignettes involved an individual was involved in a romantic infidelity and then entered group therapy to deal with this issue. Another group member makes a counterfactual statement to this individual referencing this incident. Direction of the counterfactual statement, severity of the negative event and its potential repeatability were all considered in assessing this relationship.A 2 x 2 x 2 factorial design was used. Direction of the counterfactual statement (i.e., upward, downward), event repeatability (repeatable, nonrepeatable) and severity of infidelity (low, high) all served as between-subject factors. The two dependent variables were the Positive Affect and Negative Affect subscales of the Positive and Negative Affect Scale (PANAS). Statistical analysis involved two analyses of variance (ANOVA), one for each dependent variable.No significant univariate interactions or main effects were found. In short, the results of the current study failed to support any of the author's hypotheses. The amounts of positive and negative affect that participants felt did not vary significantly as a function of counterfactual direction, severity of negative event or repeatability. It appears that the within group differences are larger than the between group differences. These results suggest that individuals' responses to other-generated counterfactual statements differ from their responses to self-generated counterfactual thoughts. / Department of Counseling Psychology and Guidance Services

<p> The complexity, subtlety, interlinking, and scale of many problems faced individually and collectively in today's rapidly changing world requires an epistemology--a way of thinking about our knowing--capable of facilitating new kinds of responses that avoid recapitulation of old ways of thinking and living. Epistemology, which implicitly provides the basis for engagement with the world via the fundamental act of distinction, must therefore be included as a central facet of any practical attempts at self/world transformation. We need to change <i>how</i> we think, not just <i> what</i> we think. The new epistemology needs to be of a higher order than the source of the problems we face. </p><p> This theoretical, transdisciplinary dissertation argues that such a new epistemology needs to be recursive and process-oriented. This means that the thoughts about thinking that it produces must explicitly follow the patterns of thinking by which those thoughts are generated. The new epistemology is therefore also phenomenological, requiring the development of a reflexivity in thinking that recursively links across two levels of order--between content and process. The result is an epistemology that is of (and for) the <i> whole</i> human being. It is an enacted (will-imbued) and aesthetic (feeling-permeated) epistemology (thinking-penetrated) that is sensitive to and integrative of material, soul, and spiritual aspects of ourselves and our world. I call this kind of epistemology <i>aesthetic</i>, because its primary characteristic is found in the phenomenological, mutually fructifying and transformative marriage between the capacity for thinking and the capacity for feeling. </p><p> Its foundations are brought forward through the confluence of multiple domains: cybernetic epistemology, the esoteric epistemology of anthroposophy (the spiritual science of Rudolf Steiner), and the philosophy of the implicit as developed by Eugene Gendlin. </p><p> The practice of aesthetic epistemology opens new phenomenal domains of experience, shedding light on relations between ontology and epistemology, mind and body, logic and thinking, as well as on the formation (and transformation) of identity, the immanence of thinking in world-processes, the existence of different types of logic, and the nature of beings, of objects, and most importantly of thinking itself and its relationship to spirit.</p>

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This thesis is a model-theoretic study of exponential differential equations in the context of differential algebra. I define the theory of a set of differential equations and give an axiomatization for the theory of the exponential differential equations of split semiabelian varieties. In particular, this includes the theory of the equations satisfied by the usual complex exponential function and the Weierstrass p-functions. The theory consists of a description of the algebraic structure on the solution sets together with necessary and sufficient conditions for a system of equations to have solutions. These conditions are stated in terms of a dimension theory; their necessity generalizes Ax’s differential field version of Schanuel’s conjecture and their sufficiency generalizes recent work of Crampin. They are shown to apply to the solving of systems of equations in holomorphic functions away from singularities, as well as in the abstract setting. The theory can also be obtained by means of a Hrushovski-style amalgamation construction, and I give a category-theoretic account of the method. Restricting to the usual exponential differential equation, I show that a “blurring” of Zilber’s pseudo-exponentiation satisfies the same theory. I conjecture that this theory also holds for a suitable blurring of the complex exponential maps and partially resolve the question, proving the necessity but not the sufficiency of the aforementioned conditions. As an algebraic application, I prove a weak form of Zilber’s conjecture on intersections with subgroups (known as CIT) for semiabelian varieties. This in turn is used to show that the necessary and sufficient conditions are expressible in the appropriate first order language.

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The past few years have witnessed a rapid growth in the use of fuzzy logic controllers for the control of processes which are complex and ill-defined. These control systems, inspired by the approximate reasoning capabilities of humans under conditions of uncertainty and imprecision, consist of linguistic 'if-then' rules which depend on fuzzy set theory for representation and evaluation using computers. Even though the fuzzy rules can be built from purely heuristic knowledge such as a human operator's control strategy, a number of difficulties face the designer of such systems. For any reasonably complex chemical process, the number of rules required to ensure adequate control in all operating regions may be extremely large. Eliciting all of these rules and ensuring their consistency and completeness can be a daunting task. An alternative to modelling the operator's response is to model the process and then to incorporate the process model into some sort of model-based control scheme. The concept of Model Based Predictive Control (MB PC) has been heralded as one of the most significant control developments in recent years. It is now widely used in the chemical and petrochemical industry and it continues to attract a considerable amount of research. Its popularity can be attributed to its many remarkable features and its open methodology. The wide range of choice of model structures, prediction horizon and optimisation criteria allows the control designer to easily tailor MBPC to his application. Features sought from such controllers include better performance, ease of tuning, greater robustness, ability to handle process constraints, dead time compensation and the ability to control nonminimum phase and open loop unstable processes. The concept of MBPC is not restricted to single-input single-output (SISO) processes. Feedforward action can be introduced easily for compensation of measurable disturbances and the use of state-space model formulation allows the approach to be generalised easily to multi-input multi-output (MIMO) systems. Although many different MBPC schemes have emerged, linear process models derived from input-output data are often used either explicitly to predict future process behaviour and/or implicitly to calculate the control action even though many chemical processes exhibit nonlinear process behaviour. It is well-recognised that the inherent nonlinearity of many chemical processes presents a challenging control problem, especially where quality and/or economic performance are important demands. In this thesis, MBPC is incorporated into a nonlinear fuzzy modelling framework. Even though a control algorithm based on a 1-step ahead predictive control strategy has initially been examined, subsequent studies focus on determining the optimal controller output using a long-range predictive control strategy. The fuzzy modelling method proposed by Takagi and Sugeno has been used throughout the thesis. This modelling method uses fuzzy inference to combine the outputs of a number of auto-regressive linear sub-models to construct an overall nonlinear process model. The method provides a more compact model (hence requiring less computations) than fuzzy modelling methods using relational arrays. It also provides an improvement in modelling accuracy and effectively overcomes the problems arising from incomplete models that characterise relational fuzzy models. Difficulties in using traditional cost function and optimisation techniques with fuzzy models have led other researchers to use numerical search techniques for determining the controller output. The emphasis in this thesis has been on computationally efficient analytically derived control algorithms. The performance of the proposed control system is examined using simulations of the liquid level in a tank, a continuous stirred tank reactor (CSTR) system, a binary distillation column and a forced circulation evaporator system. The results demonstrate the ability of the proposed system to outperform more traditional control systems. The results also show that inspite of the greatly reduced computational requirement of our proposed controller, it is possible to equal or better the performance of some of the other fuzzy model based control systems that have been proposed in the literature. It is also shown in this thesis that the proposed control algorithm can be easily extended to address the requirements of time-varying processes and processes requiring compensation for disturbance inputs and dead times. The application of the control system to multivariable processes and the ability to incorporate explicit constraints in the optimisation process are also demonstrated.

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The dynamic characteristics of autonomous underwater vehicles (AUVs) present a control problem that classical methods cannot often accommodate easily. Fundamentally, AUV dynamics are highly non-linear, and the relative similarity between the linear and angular velocities about each degree of freedom means that control schemes employed within other flight vehicles are not always applicable. In such instances, intelligent control strategies offer a more sophisticated approach to the design of the control algorithm. Neurofuzzy control is one such technique, which fuses the beneficial properties of neural networks and fuzzy logic in a hybrid control architecture. Such an approach is highly suited to development of an autopilot for an AUV. Specifically, the adaptive network-based fuzzy inference system (ANFIS) is discussed in Chapter 4 as an effective new approach for neurally tuning course-changing fuzzy autopilots. However, the limitation of this technique is that it cannot be used for developing multivariable fuzzy structures. Consequently, the co-active ANFIS (CANFIS) architecture is developed and employed as a novel multi variable AUV autopilot within Chapter 5, whereby simultaneous control of the AUV yaw and roll channels is achieved. Moreover, this structure is flexible in that it is extended in Chapter 6 to perform on-line control of the AUV leading to a novel autopilot design that can accommodate changing vehicle pay loads and environmental disturbances. Whilst the typical ANFIS and CANFIS structures prove effective for AUV control system design, the well known properties of radial basis function networks (RBFN) offer a more flexible controller architecture. Chapter 7 presents a new approach to fuzzy modelling and employs both ANFIS and CANFIS structures with non-linear consequent functions of composite Gaussian form. This merger of CANFIS and a RBFN lends itself naturally to tuning with an extended form of the hybrid learning rule, and provides a very effective approach to intelligent controller development.

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