An exploration of transformation theory and the western tradition: a critical evaluation of a graduate studies class

This qualitative study is an exploration of transformation theory, the Western tradition, and a critical evaluation of a graduate studies class at a university. It is an exploration of assumptions that are embedded in experience, that influence the experience and provide meaning about the experience. An attempt has been made to identify assumptions that are embedded in Western experience and connect them with assumptions that shape the graduate class experience. The focus is on assumptions that facilitate and impede large group discussions. Jungian psychology of personality type and archetype and developmental psychology is used to analyze the group experience. The pragmatic problem solving model, developed by Knoop, is used to guide thinking about the Western tradition. It is used to guide the analysis, synthesis and writing of the experience of the graduate studies class members. A search through Western history, philosophy. and science revealed assumptions about the nature of truth, reality, and the self. Assumptions embedded in Western thinking about the subject-object relationship, unity and diversity are made explicit. An attempt is made to identify Western tradition assumptions underlying transformation theory. The critical evaluation of the graduate studies class experience focuses upon issues associated with group process, self-directed learning, the educator-learner transaction and the definition of adult education. The advantages of making implicit assumptions explicit is explored.

The shifting terrain of feminist theory and activism : university-based women's centres and third wave feminism

This thesis, based on the results of an organizational ethnography of a university-based feminist organization in Southern Ontario (the Centre), traces how third wave feminism is being constituted in the goals, initiatives, mandate, organizational structure, and overall culture of university-based feminist organizations. I argue that, from its inception, the meanings and goals of the Centre have been contested through internal critique, reflection, and discussion inspired by significant shifts in feminist theory that challenge the fundamental principles of second wave feminism. I identify a major shift in the development and direction of the Centre that occurs in two distinct phases. The first phase of the shift occurs with the emergence of an antioppression framework, which broadens the Centre's mandate beyond gender and sexism to consider multiple axes of identity and oppression that affect women's lives. The second phase of this shift is characterized by a focus on (trans) inclusion and accessibility and has involved changing the Centre's name so that it is no longer identified as a women's centre in order to reflect more accurately its focus on mUltiple axes of identity and oppression. Along with identifying two phases of a major shift in the direction of the Centre, I trace two discourses about its development. The dominant discourse of the Centre's development is one of progress and evolution. The dominant discourse characterizes the Centre as a dynamic feminist organization that consistently strives to be more inclusive and diverse. The reverse discourse undermines the dominant discourse by emphasizing that, despite the Centre's official attempts to be inclusive and to build diversity, little has actually changed, leaving women of colour marginalized in the Centre's dominant culture of whiteness. This research reveals that, while many of their strategies have unintended (negative) consequences, members of the Centre are working to build an inclusive politics of resistance that avoids the mistakes of earlier feminist movements and organizations. These members, along with other activists, actively constitute third wave feminism in a process that is challenging, contradictory, and often painful. A critical analysis of this process and the strategies it involves provides an opportunity for activists to reflect on their experiences and develop new strategies in an effort to further struggles for social justice and equity.

The historical game-changes in the philosophy of devotion and caste as used and misused by the Bhagavad-gita

This thesis considers that the purport of the Bhagavadgita is to prioritize the philosophy of loving devotion to God (bhakti), not the propagation of color-coded-caste (varna system). The distinction between bhakti and caste becomes clear when one sees their effect on human life and on the society. Jnana and karma, two of the other polarities with which the Gita contends, finally support bhakti towards betterment, not deterioration, if done selflessly and with balance. Caste, however, is a totally different tension, which is always detrimental to the well-being of the person and the society. In the Gita, the devotees' mystical or emotional love of, God apprehends their ~ oneness with the Supreme God and with all beings, and transcends the pitiless segregation of the caste system, and opens the path of salvation to all irrespective of race, color, caste, class or gender in life. In spite of much opposition from orthodoxy, the bhakti movement spread allover India, and bhakti itself rose to the level of orthodoxy and has become the faith of millions of people especially of the south, and surprisingly, of even of those of the so called highest caste. And yet, caste still remains as an indelible mark of every Hindu, even after they change their religion. Although caste is less venomous now, it is still openly present in all walks of Indian life and shows up its ugly head at important moments such as marriage, elections for public office, admission to school or employment. True, bhakti is the antidote for. caste; but only real bhakti can remove caste completely, not mere lip-service to it. This thesis claims that bhakti is the deliberate major thrust of the teaching of the Gita while caste seems to be a contradiction of this thrust.

The association of faculty's teaching philosophy and teaching behaviour, and critical thinking and self- direction in learning

The intent in this study was to investigate in what ways teachers· beliefs about education and teaching are expressed in the specific teaching behaviours they employ, and whether teaching behaviours, as perceived by their students, are correlated with students· critical thinking and self-directed learning. To this end the relationships studied were: among faCUlty members· philosophy of teaching, locus of control orientation, psychological type, and observed teaching behaviour; and among students· psychological type, perceptions of teaching behaviour, self-directed learning readiness, and critical thinking. The overall purpose of the study was to investigate whether the implicit goals of higher education, critical thinking and self-direction, were actually accounted for in the university classroom. The research was set within the context of path-goal theory, adapted from the leadership literature. Within this framework, Mezirow·s work on transformative learning, including the influences of Habermas· writings, was integrated to develop a theoretical perspective upon which to base the research methodology. Both qualitative and quantitative methodologies were incorporated. Four faCUlty and a total of 142 students participated in the study. Philosophy of teaching was described through faCUlty interviews and completion of a repertory grid. Faculty completed a descriptive locus of control scale, and a psychological type test. Observations of their teaching behaviour were conducted. Students completed a Teaching Behaviour Assessment Scale, the Self-Directed Learning Readiness Scale, a psychological type test, and the Watson-Glaser Critical Thinking Appraisal. A small sample of students were interviewed. Follow-up discussions with faculty were used to validate the interview, observation, teaching behaviour, and repertory grid data. Results indicated that some discrepancies existed between faculty's espoused philosophy of teaching and their observed teaching behaviour. Instructors' teaching behaviour, however, was a function of their personal theory of practice. Relationships were found between perceived teaching behaviour and students· self-directed learning and critical thinking, but these varied across situations, as would be predicted from path-goal theory. Psychological type of students and instructor also accounted for some of the variability in the relationships studied. Student psychological type could be shown as a partial predictor of self-directed learning readiness. The results were discussed in terms of theory development and implications for further research and practice.

Kierkegaardian intersubjectivity and the question of ethics and responsibility

Kierkegaardian Intersubjectivity and the Question of Ethics and Responsibility By Kevin Krumrei. Kierkegaard's contributions to philosophy are generally admitted and recognized as valuable in the history of Western philosophy, both as one of the great anti-Hegelians, as the founder (arguably) of existentialism, and as a religious thinker. However valid this may be, there is similarly a generally admitted critique of Kierkegaard in the Western tradition, that Kierkegaard's philosophy of the development of the self leads the individual into an isolated encounter with God, to the abandonment of the social context. In other words, a Kierkegaardian theory of intersubjectivity is a contradiction in terms. This is voiced eloquently by Emmanuel Levinas, among others. However, Levinas' own intersubjective ethics bears a striking resemblance to Kierkegaard's, with respect to the description and formulation of the basic problem for ethics: the problem of aesthetic egoism. Further, both Kierkegaard and Levinas follow similar paths in responding to the problem, from Kierkegaard's reduplication in Works of Love, to Levinas' notion of substitution in Otherwise than Being. In this comparison, it becomes evident that Levinas' reading of Kierkegaard is mistaken, for Kierkegaard's intersubjective ethics postulates, in fact, the inseparability and necessity of the self s responsible relation to others in the self s relation to God, found in the command, "you shall love your neighbour as yourself."

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Husserl's approach to transcendental intersubjectivity

It is our intention in the course of the development of this thesis to give an account of how intersubjectivity is "eidetically" constituted by means of the application of the phenomenological reduction to our experience in the context of the thought of Edmund Husserl; contrasted with various representative thinkers in what H. Spiegelberg refers to as "the wider scene" of phenomenology. That is to say, we intend to show those structures of both consciousness and the relation which man has to the world which present themselves as the generic conditions for the possibility of overcoming our "radical sol itude" in order that we may gain access to the mental 1 ife of an Other as other human subject. It is clear that in order for us to give expression to these accounts in a coherent manner, along with their relative merits, it will be necessary to develop the common features of any phenomenological theory of consdousness whatever. Therefore, our preliminary inquiry, subordinate to the larger theme, shall be into some of the epistemological results of the application of the phenomenological method used to develop a transcendental theory of consciousness. Inherent in this will be the deliniation of the exigency for making this an lIintentional ll theory. We will then be able to see how itis possible to overcome transcendentally the Other as an object merely given among other merely given objects, and further, how this other is constituted specifically as other ego. The problem of transcendental intersubjectivity and its constitution in experience can be viewed as one of the most compelling, if not the most polemical of issues in phenomenology. To be sure, right from the beginning we are forced to ask a number of questions regarding Husserl's responses to the problem within the context of the methodological genesis of the Cartesian Meditations, and The Crisis of European Sciences and Transcendental Phenomenology. This we do in order to set the stage for amplification. First, we ask, has Husserl lived up to his goal, in this connexion, of an apodictic result? We recall that in his Logos article of 1911 he adminished that previous philosophy does not have at its disposal a merely incomplete and, in particular instances, imperfect doctrinal system; it simply has none whatever. Each and every question is herein controverted, each position is a matter of individual conviction, of the interpretation given byaschool, of a "point of view". 1. Moreover in the same article he writes that his goal is a philosophical system of doctrine that, after the gigantic preparatory work. of generations, really be- . gins from the ground up with a foundation free from doubt and rises up like any skilful construction, wherein stone is set upon store, each as solid as the other, in accord with directive insights. 2. Reflecting upon the fact that he foresaw "preparatory work of generations", we perhaps should not expect that he would claim that his was the last word on the matter of intersubjectivity. Indeed, with 2. 'Edmund Husserl, lIPhilosophy as a Rigorous Science" in Phenomenology and theCrisis6fPhilosophy, trans". with an introduction by Quentin Lauer (New York.: Harper & Row, 1965) pp. 74 .. 5. 2Ibid . pp. 75 .. 6. 3. the relatively small amount of published material by Husserl on the subject we can assume that he himself was not entirely satisfied with his solution. The second question we have is that if the transcendental reduction is to yield the generic and apodictic structures of the relationship of consciousness to its various possible objects, how far can we extend this particular constitutive synthetic function to intersubjectivity where the objects must of necessity always remain delitescent? To be sure, the type of 'object' here to be considered is unlike any other which might appear in the perceptual field. What kind of indubitable evidence will convince us that the characteristic which we label "alter-ego" and which we attribute to an object which appears to resemble another body which we have never, and can never see the whole of (namely, our own bodies), is nothing more than a cleverly contrived automaton? What;s the nature of this peculiar intentional function which enables us to say "you think just as I do"? If phenomenology is to take such great pains to reduce the takenfor- granted, lived, everyday world to an immanent world of pure presentation, we must ask the mode of presentation for transcendent sub .. jectivities. And in the end, we must ask if Husserl's argument is not reducible to a case (however special) of reasoning by analogy, and if so, tf this type of reasoning is not so removed from that from whtch the analogy is made that it would render all transcendental intersubjective understandtng impos'sible? 2. HistoticalandEidetic Priority: The Necessity of Abstraction 4. The problem is not a simple one. What is being sought are the conditions for the poss ibili:ty of experi encing other subjects. More precisely, the question of the possibility of intersubjectivity is the question of the essence of intersubjectivity. What we are seeking is the absolute route from one solitude to another. Inherent in this programme is the ultimate discovery of the meaning of community. That this route needs be lIabstract" requires some explanation. It requires little explanation that we agree with Husserl in the aim of fixing the goal of philosophy on apodictic, unquestionable results. This means that we seek a philosophical approach which is, though, not necessarily free from assumptions, one which examines and makes explicit all assumptions in a thorough manner. It would be helpful at this point to distinguish between lIeidetic ll priority, and JlhistoricallJpriority in order to shed some light on the value, in this context, of an abstraction.3 It is true that intersubjectivity is mundanely an accomplished fact, there havi.ng been so many mi.llions of years for humans to beIt eve in the exi s tence of one another I s abili ty to think as they do. But what we seek is not to study how this proceeded historically, but 3Cf• Maurice Natanson;·TheJburne in 'Self, a Stud in Philoso h and Social Role (Santa Cruz, U. of California Press, 1970 . rather the logical, nay, "psychological" conditions under which this is possible at all. It is therefore irrelevant to the exigesis of this monograph whether or not anyone should shrug his shoulders and mumble IIwhy worry about it, it is always already engaged". By way of an explanation of the value of logical priority, we can find an analogy in the case of language. Certainly the language 5. in a spoken or written form predates the formulation of the appropriate grammar. However, this grammar has a logical priority insofar as it lays out the conditions from which that language exhibits coherence. The act of formulating the grammar is a case of abstraction. The abstraction towards the discovery of the conditions for the poss; bi 1 ity of any experiencing whatever, for which intersubjective experience is a definite case, manifests itself as a sort of "grammar". This "grammar" is like the basic grammar of a language in the sense that these "rulesil are the ~ priori conditions for the possibility of that experience. There is, we shall say, an "eidetic priority", or a generic condition which is the logical antecedent to the taken-forgranted object of experience. In the case of intersubjectivity we readily grant that one may mundanely be aware of fellow-men as fellowmen, but in order to discover how that awareness is possible it is necessary to abstract from the mundane, believed-in experience. This process of abstraction is the paramount issue; the first step, in the search for an apodictic basis for social relations. How then is this abstraction to be accomplished? What is the nature of an abstraction which would permit us an Archimedean point, absolutely grounded, from which we may proceed? The answer can be discovered in an examination of Descartes in the light of Husserl's criticism. 3. The Impulse for Scientific Philosophy. The Method to which it Gives Rise. 6. Foremost in our inquiry is the discovery of a method appropriate to the discovery of our grounding point. For the purposes of our investigations, i.e., that of attempting to give a phenomenological view of the problem of intersubjectivity, it would appear to be of cardinal importance to trace the attempt of philosophy predating Husserl, particularly in the philosophy of Descartes, at founding a truly IIscientific ll philosophy. Paramount in this connexion would be the impulse in the Modern period, as the result of more or less recent discoveries in the natural sciences, to found philosophy upon scientific and mathematical principles. This impulse was intended to culminate in an all-encompassing knowledge which might extend to every realm of possible thought, viz., the universal science ot IIMathexis Universalis ll •4 This was a central issue for Descartes, whose conception of a universal science would include all the possible sciences of man. This inclination towards a science upon which all other sciences might be based waS not to be belittled by Husserl, who would appropriate 4This term, according to Jacab Klein, was first used by Barocius, the translator of Proclus into Latin, to designate the highest mathematical discipline. . 7. it himself in hopes of establishing, for the very first time, philosophy as a "rigorous science". It bears emphasizing that this in fact was the drive for the hardening of the foundations of philosophy, the link between the philosophical projects of Husserl and those of the philosophers of the modern period. Indeed, Husserl owes Descartes quite a debt for indicating the starting place from which to attempt a radical, presupositionless, and therefore scientific philosophy, in order not to begin philosophy anew, but rather for the first time.5 The aim of philosophy for Husserl is the search for apodictic, radical certitude. However while he attempted to locate in experience the type of necessity which is found in mathematics, he wished this necessity to be a function of our life in the world, as opposed to the definition and postulation of an axiomatic method as might be found in the unexpurgated attempts to found philosophy in Descartes. Beyond the necessity which is involved in experiencing the world, Husserl was searching for the certainty of roots, of the conditi'ons which underl ie experience and render it pOssible. Descartes believed that hi~ MeditatiOns had uncovered an absolute ground for knowledge, one founded upon the ineluctable givenness of thinking which is present even when one doubts thinking. Husserl, in acknowledging this procedure is certainly Cartesian, but moves, despite this debt to Descartes, far beyond Cartesian philosophy i.n his phenomenology (and in many respects, closer to home). 5Cf. Husserl, Philosophy as a Rigorous Science, pp. 74ff. 8 But wherein lies this Cartesian jumping off point by which we may vivify our theme? Descartes, through inner reflection, saw that all of his convictions and beliefs about the world were coloured in one way or another by prejudice: ... at the end I feel constrained to reply that there is nothing in a all that I formerly believed to be true, of which I cannot in some measure doubt, and that not merely through want of thought or through levity, but for reasons which are very powerful and maturely considered; so that henceforth I ought not the less carefully to refrain from giving credence to these opinions than to that which is manifestly false, if I desire to arrive at any certainty (in the sciences). 6 Doubts arise regardless of the nature of belief - one can never completely believe what one believes. Therefore, in order to establish absolutely grounded knowledge, which may serve as the basis fora "universal Science", one must use a method by which one may purge oneself of all doubts and thereby gain some radically indubitable insight into knowledge. Such a method, gescartes found, was that, as indicated above by hi,s own words, of II radical doubt" which "forbids in advance any judgemental use of (previous convictions and) which forbids taking any position with regard to their val idi'ty. ,,7 This is the method of the "sceptical epoche ll , the method of doubting all which had heretofor 6Descartes,Meditations on First Philosophy, first Med., (Libera 1 Arts Press, New York, 1954) trans. by L. LaFl eur. pp. 10. 7Husserl ,CrisiS of Eliroeari SCiences and Trariscendental Phenomenology, (Northwestern U. Press, Evanston, 1 7 ,p. 76. 9. been considered as belonging to the world, including the world itself. What then is left over? Via the process of a thorough and all-inclusive doubting, Descartes discovers that the ego which performs the epoche, or "reduction", is excluded from these things which can be doubted, and, in principle provides something which is beyond doubt. Consequently this ego provides an absolute and apodictic starting point for founding scientific philosophy. By way of this abstention. of bel ief, Desca'rtes managed to reduce the worl d of everyday 1 ife as bel ieved in, to mere 'phenomena', components of the rescogitans:. Thus:, having discovered his Archimedean point, the existence of the ego without question, he proceeds to deduce the 'rest' of the world with the aid of innate ideas and the veracity of God. In both Husserl and Descartes the compelling problem is that of establ ishing a scientific, apodictic phi'losophy based upon presuppos itionless groundwork .. Husserl, in thi.s regard, levels the charge at Descartes that the engagement of his method was not complete, such that hi.S: starting place was not indeed presupositionless, and that the validity of both causality and deductive methods were not called into question i.'n the performance of theepoche. In this way it is easy for an absolute evidence to make sure of the ego as: a first, "absolute, indubitablyexisting tag~end of the worldll , and it is then only a matter of inferring the absolute subs.tance and the other substances which belon.g to the world, along with my own mental substance, using a logically val i d deductive procedure. 8 8Husserl, E.;' Cartesian 'Meditation;, trans. Dorion Cairns (Martinus Nijhoff, The Hague, 1970), p. 24 ff.

Native women, theory and research : contexts and contestations

In this thesis I outline a critical approach to interpreting the considerable academic literature on Aboriginal women in North America. I locate the scholarship concerning Native women within an understanding of three developments related to a philosophy of science: (I) paradigmatic shifts concerning the philosophy of science, (2) materialist-idealist debates and (3) transitions in feminist theory characterized by what is tenned the shift from second to third wave feminism. My exploration of emergent themes suggests that the elements indicated above provide overlapping frameworks within which most scholarship about Indigenous women is positioned. I illustrate my finding that employing critical discourse analysis and postcolonial feminism as both method and theory provides a useful approach in attending to intersecting experiences of 'race, class, and gender.' I view these intersecting experiences as central to the socio-political positioning of Indigenous women within contemporary feminist theorizing. I conclude my thesis by reflecting on the conceptual struggles I experienced in fonnulating and organizing the thesis and the significance of my underlying epistemological position and value-orientation as both a feminist and Native woman.

Buddhism and the earth : environmental thought in early Buddhist philosophy

Introduction Fundamental to the philosophy of Buddhism, is the insight that there is "unsatisfactohness" (dukkha) in the world and that it can be eliminated through the practice of the Noble Eight Fold Path. Buddhism also maintains that the world as we experience and entities that exist are bereft of any substantiality. Instead existence is manifest through dependent origination. All things are conditional; nothing is permanent. However, inherent in this dependent existence is the interconnectedness of all beings and their subjection to the cosmic law of karma. Part of cultivating the Eight Fold path includes a deep compassion for all other living things, 'trapped' within this cycle of dependent origination. This compassion or empathy (karuna) is crucial to the Buddhist path to enlightenment. It is this emphasis on karuna that shows itself in Mahayana Buddhism with respect to the theory of the boddhisatva (or Buddha-to-be) since the boddhisatva willingly postpones his/her own enlightenment to help others on the same path. One of the ramifications of the theory of dependent origination is that there is no anthropocentric bias placed on humans over the natural world. Paradoxically the doctrine of non-self becomes an ontology within Buddhism, culminating in the Mayahana realization that a common boundary exists between samsara and nirvana. Essential to this ontology is the life of dharma or a moral life. Ethics is not separated from ontology. As my thesis will show, this basic outlook of Buddhism has implications toward our understanding of the Buddhist world-view with respect to the current human predicament concerning the environment. While humans are the only ones who can 4 attain "Buddhahood", it is because of our ability to understand what it means to follow the Eight fold path and act accordingly. Because of the interconnectedness of all entities {dharmas), there is an ontological necessity to eliminate suffering and 'save the earth' because if we allow the earth to suffer, we ALL suffer. This can be understood as an ethical outlook which can be applied to our interaction with and treatment of the natural environment or environment in the broadest sense, not just trees plants rocks etc. It is an approach to samsara and all within it. It has been argued that there is no ontology in Buddhism due to its doctrine of "non-self". However, it is a goal of this thesis to argue that there does exist an original ontology in Buddhism; that according to it, the nature of Being is essentially neither "Being nor non-being nor not non-being" as illustrated by Nagarjuna. Within this ontology is engrained an ethic or 'right path' (samma marga) that is fundamental to our being and this includes a compassionate relationship to our environment. In this dissertation I endeavour to trace the implications that the Buddhist worldview has for the environmental issues that assail us in our age of technology. I will explore questions such as: can the Buddhist way of thinking help us comprehend and possibly resolve the environmental problems of our day and age? Are there any current environmental theories which are comparable to or share common ground with the classical Buddhist doctrines? I will elucidate some fundamental doctrines of early Buddhism from an environmental perspective as well as identify some comparable modern environmental theories such as deep ecology and general systems theory, that seem to share in the wisdom of classical Buddhism and have much to gain from a deeper appreciation of Buddhism.

Towards automated derivation in the theory of allegories

We provide an algorithm that automatically derives many provable theorems in the equational theory of allegories. This was accomplished by noticing properties of an existing decision algorithm that could be extended to provide a derivation in addition to a decision certificate. We also suggest improvements and corrections to previous research in order to motivate further work on a complete derivation mechanism. The results presented here are significant for those interested in relational theories, since we essentially have a subtheory where automatic proof-generation is possible. This is also relevant to program verification since relations are well-suited to describe the behaviour of computer programs. It is likely that extensions of the theory of allegories are also decidable and possibly suitable for further expansions of the algorithm presented here.

A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

'To do justice and judgement' : the place of passion in public life

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 P65 F47 2003

GA approach for finding Rough Set decision rules based on bireducts

Feature selection plays an important role in knowledge discovery and data mining nowadays. In traditional rough set theory, feature selection using reduct - the minimal discerning set of attributes - is an important area. Nevertheless, the original definition of a reduct is restrictive, so in one of the previous research it was proposed to take into account not only the horizontal reduction of information by feature selection, but also a vertical reduction considering suitable subsets of the original set of objects. Following the work mentioned above, a new approach to generate bireducts using a multi--objective genetic algorithm was proposed. Although the genetic algorithms were used to calculate reduct in some previous works, we did not find any work where genetic algorithms were adopted to calculate bireducts. Compared to the works done before in this area, the proposed method has less randomness in generating bireducts. The genetic algorithm system estimated a quality of each bireduct by values of two objective functions as evolution progresses, so consequently a set of bireducts with optimized values of these objectives was obtained. Different fitness evaluation methods and genetic operators, such as crossover and mutation, were applied and the prediction accuracies were compared. Five datasets were used to test the proposed method and two datasets were used to perform a comparison study. Statistical analysis using the one-way ANOVA test was performed to determine the significant difference between the results. The experiment showed that the proposed method was able to reduce the number of bireducts necessary in order to receive a good prediction accuracy. Also, the influence of different genetic operators and fitness evaluation strategies on the prediction accuracy was analyzed. It was shown that the prediction accuracies of the proposed method are comparable with the best results in machine learning literature, and some of them outperformed it.