Acceptance and commitment therapy (ACT) is an empirically supported cognitive behavioral therapy. The ACT model is designed around a set of six core processes utilized to increase psychological flexibility. Engagement with values, one of the six core processes, is associated with several indicators of well-being. However, recent reviews of ACT values measures from experts in the field raised concerns that current instruments do not adequately assess the values process. The current study examined the structure and psychometric properties of a new values measure, titled the Valued Living Questionnaire—Online version (VLQ-O), that was developed from considerations raised in these reviews. The results of an EFA indicated that the VLQ-O produced a three-factor structure comprised of Values Flexibility, Values Inflexibility, and Values Obligations. The Activity and Preferred Activity scores did not load consistently onto any discernable factor. The subscales of the VLQ-O produced poor internal consistency. The scores for Activity and Values Flexibility subscales correlated positively with measures of well-being and negatively with measures of psychological distress. Additionally, these subscales were significantly positively related to MPFI Flexibility and VQ Progress and well as negatively related to MPFI Inflexibility and VQ Obstruction. Values Inflexibility and Values Obligation correlated positively with measures of psychological distress and negatively with measures of well-being. The Values Obligation subscale did not correlate with social desirability. Multiple subscales of the VLQ-O demonstrated significant correlations with multiple subscales of the BFI. Additionally, the VLQ-O established predictive validity for measures of psychological distress and well-being. Further, it established improvements in predictive validity for flourishing and psychological distress when compared to the Valuing Questionnaire (VQ). Overall, the findings from this study provide some supportive preliminary evidence for the validity of the VLQ-O.

The purpose of this paper is to make a suggestion to deontic logic: Respect Hume\'s Law, the answer to the is-ought problem that says that all ought-talk is completely cut off from is-talk. Most deontic logicians have sought another solution: Namely, the solution that says that we can bridge the is-ought gap. Thus, a century\'s worth of research into these normative systems of logic has lead to many attempts at doing just that. At the same time, the field of deontic logic has come to be plagued with paradox. My argument essentially depends upon there being a substantive relation between this betrayal of Hume and the plethora of paradoxes that have appeared in two-adic (binary normative operator), one-adic (unary normative operator), and zero-adic (constant normative operator) deontic systems, expressed in the traditions of von Wright, Kripke, and Anderson, respectively. My suggestion has two motivations: First, to rid the philosophical literature of its puzzles and second, to give Hume\'s Law a proper formalization. Exploring the issues related to this project also points to the idea that maybe we should re-engineer (e.g., further generalize) our classical calculus, which might involve the adoption of many-valued logics somewhere down the line. / Master of Arts

Spectral techniques in digital logic design have been known for more than thirty years. They have been used for Boolean function classification, disjoint decomposition, parallel and serial linear decomposition, spectral translation synthesis (extraction of linear pre- and post-filters), multiplexer synthesis, prime implicant extraction by spectral summation, threshold logic synthesis, estimation of logic complexity, testing, and state assignment. This dissertation resolves many important issues concerning the efficient application of spectral methods used in the computer-aided design of digital circuits. The main obstacles in these applications were, up to now, memory requirements for computer systems and lack of the possibility of calculating spectra directly from Boolean equations. By using the algorithms presented here these obstacles have been overcome. Moreover, the methods presented in this dissertation can be regarded as representatives of a whole family of methods and the approach presented can be easily adapted to other orthogonal transforms used in digital logic design. Algorithms are shown for Adding, Arithmetic, and Reed-Muller transforms. However, the main focus of this dissertation is on the efficient computer calculation of Rademacher-Walsh spectra of Boolean functions, since this particular ordering of Walsh transforms is most frequently used in digital logic design. A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON- and DC- cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from non-disjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. By such an approach each spectral coefficient can be calculated separately or all the coefficients can be calculated in parallel. These advantages are absent in the existing methods. The possibility of calculating only some coefficients is very important since there are many spectral methods in digital logic design for which the values of only a few selected coefficients are needed. Most of the current methods used in the spectral domain deal only with completely specified Boolean functions. On the other hand, all of the algorithms introduced here are valid, not only for completely specified Boolean functions, but for functions with don't cares. Don't care minterms are simply represented in the form of disjoint cubes. The links between spectral and classical methods used for designing digital circuits are described. The real meaning of spectral coefficients from Walsh and other orthogonal spectra in classical logic terms is shown. The relations presented here can be used for the calculation of different transforms. The methods are based on direct manipulations on Karnaugh maps. The conversion start with Karnaugh maps and generate the spectral coefficients. The spectral representation of multiple-valued input binary functions is proposed here for the first time. Such a representation is composed of a vector of Walsh transforms each vector is defined for one pair of the input variables of the function. The new representation has the advantage of being real-valued, thus having an easy interpretation. Since two types of codings of values of binary functions are used, two different spectra are introduced. The meaning of each spectral coefficient in classical logic terms is discussed. The mathematical relationships between the number of true, false, and don't care minterms and spectral coefficients are stated. These relationships can be used to calculate the spectral coefficients directly from the graphical representations of binary functions. Similarly to the spectral methods in classical logic design, the new spectral representation of binary functions can find applications in many problems of analysis, synthesis, and testing of circuits described by such functions. A new algorithm is shown that converts the disjoint cube representation of Boolean functions into fixed-polarity Generalized Reed-Muller Expansions (GRME). Since the known fast algorithm that generates the GRME, based on the factorization of the Reed-Muller transform matrix, always starts from the truth table (minterms) of a Boolean function, then the described method has advantages due to a smaller required computer memory. Moreover, for Boolean functions, described by only a few disjoint cubes, the method is much more efficient than the fast algorithm. By investigating a family of elementary second order matrices, new transforms of real vectors are introduced. When used for Boolean function transformations, these transforms are one-to-one mappings in a binary or ternary vector space. The concept of different polarities of the Arithmetic and Adding transforms has been introduced. New operations on matrices: horizontal, vertical, and vertical-horizontal joints (concatenations) are introduced. All previously known transforms, and those introduced in this dissertation can be characterized by two features: "ordering" and "polarity". When a transform exists for all possible polarities then it is said to be "generalized". For all of the transforms discussed, procedures are given for generalizing and defining for different orderings. The meaning of each spectral coefficient for a given transform is also presented in terms of standard logic gates. There exist six commonly used orderings of Walsh transforms: Hadamard, Rademacher, Kaczmarz, Paley, Cal-Sal, and X. By investigating the ways in which these known orderings are generated the author noticed that the same operations can be used to create some new orderings. The generation of two new Walsh transforms in Gray code orderings, from the straight binary code is shown. A recursive algorithm for the Gray code ordered Walsh transform is based on the new operator introduced in this presentation under the name of the "bi-symmetrical pseudo Kronecker product". The recursive algorithm is the basis for the flow diagram of a constant geometry fast Walsh transform in Gray code ordering. The algorithm is fast (N 10g2N additions/subtractions), computer efficient, and is implemented

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The introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of lattice-valued convergence spaces; the category of lattice-valued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesian-closed, and extensional. Properties of quotient maps between objects in this category are investigated in this work; in particular, one of our principal results shows that quotient maps are productive under arbitrary products. A category of lattice-valued interior operators is defined and studied as well. Axioms are given in order for this category to be isomorphic to the category whose objects consist of all the stratified, lattice-valued, pretopological convergence spaces. Adding a lattice-valued convergence structure to a group leads to the creation of a new category whose objects are called lattice-valued convergence groups, and whose morphisms are all the continuous homomorphisms between objects. The latter category is studied and results related to separation properties are obtained. For the special lattice , continuous actions of a convergence semigroup on convergence spaces are investigated; in particular, invariance properties of actions as well as properties of a generalized quotient space are presented.

The Fundamental Theorem of Algebra is a useful tool in determining the number of zeros of complex-valued polynomials and rational functions. It does not, however, apply to complex-valued harmonic polynomials and rational functions generally. In this thesis, we determine behaviors of the family of complex-valued harmonic functions $f_{c}(z) = z^{n} + \frac{c}{\overline{z}^{k}} - 1$ that defy intuition for analytic polynomials. We first determine the sum of the orders of zeros by using the harmonic analogue of Rouch\'e's Theorem. We then determine useful geometry of the critical curve and its image in order to count winding numbers by applying the harmonic analogue of the Argument Principle. Combining these results, we fully determine the number of zeros of $f_{c}$ for $c > 0$.

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The purpose of this paper is two-fold; we shall first establish a complete existential theory of functions of one real variable with respect to continuity, uniform continuity, absolute continuity, bounded variation, and Lipschitz condition, and second we shall study set-functions in a similar manner, except that the properties to be considered will be continuity, absolute continuity, bounded variation, and additivity.