We first present a realistic framework for quantum probability theory based on the path integral formalism of quantum mechanics and illustrate this framework by constructing a model that describes a quantum particle evolving in a discrete space-time lattice. We then present a finite model for describing the internal dynamics of “elementary particles” and show that this model gives the standard particle classification scheme and successfully predicts particle masses.

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are given.

We develop the concept of quantum probability based on ideas of R. Feynman. The general guidelines of quantum probability are translated into rigorous mathematical definitions. We then compare the resulting framework with that of operational statistics. We discuss various relationship between measurements and define quantum stochastic processes. It is shown that quantum probability includes both conventional probability theory and traditional quantum mechanics. Discrete quantum systems, transition amplitudes, and discrete Feynman amplitudes are treated. We close with some examples that illustrate previously (...) defined concepts. (shrink)

Fuzzy amplitude densities are employed to obtain probability distributions for measurements that are not perfectly accurate. The resulting quantum probability theory is motivated by the path integral formalism for quantum mechanics. Measurements that are covariant relative to a symmetry group are considered. It is shown that the theory includes traditional as well as stochastic quantum mechanics.

A D-algebra is a generalization of a D-poset in which a partial order is not assumed. However, if a D-algebra is equipped with a natural partial order, then it becomes a D-poset. It is shown that D-algebras and effect algebras are equivalent algebraic structures. This places the partial operation ⊝ for a D-algebra on an equal footing with the partial operation ⊕ for an effect algebra. An axiomatic structure called an effect stale-space is introduced. Such spaces provide an operational interpretation (...) for the partial operations ⊕ and ⊝. Finally, a relationship between effect-state spaces and torsion free interval effect algebras is demonstrated. (shrink)

The concept of an effect test space, which is equivalent to a D-test space of Dvurečenskij and Pulmannová, is introduced. Connections between effect test space. (E-test space, for short) morphisms, and event-morphisms as well as between algebraic E-test spaces and effect algebras, are studied. Bimorphisms and E-test space tensor products are considered. It is shown that any E-test space admits a unique (up to an isomorphism) universal group and that this group, considered as a test group, determines the E-test space (...) uniquely (up to an isomorphism). (shrink)

This paper develops a theory of quantum automata and their slightly more general versions, q-automata. Quantum languages and η-quantum languages, 0≤η<1, are studied. Functions that can be realized as probability maps for q-automata are characterized. Quantum grammars are discussed and it is shown that quantum languages are precisely those languages that are induced by a quantum grammar. A quantum pumping lemma is employed to show that there are regular languages that are not η-quantum, 0≤η<1.

We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.

State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under which it is performed. Each context provides a viewpoint of the quantum system being measured. This gives only a partial picture of the system which may be distorted and in order to obtain a total accurate picture, various contexts need to be employed. We first (...) discuss some basic definitions and results concerning quantum channels. We briefly describe the relationship between this work and ontological models that form the basis for contextuality studies. We then consider properties of channels and contexts. For example, we show that the set of sharp channels can be given a natural partial order in which contexts are the smallest elements. We also study properties of channel maps. The last section considers mutually unbiased contexts. These are related to mutually unbiased bases which have a large current literature. Finally, we connect them to completely random channel maps. (shrink)

Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test (...) outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin. (shrink)

We first define a class of processes which we call regular quantum Markov processes. We next prove some basic results concerning such processes. A method is given for constructing quantum Markov processes using transition amplitude kernels. Finally we show that the Feynman path integral formalism can be clarified by approximating it with a quantum stochastic process.

We present a realistic model in which spin measurements are represented by functions. By employing a simple amplitude density, we derive the usual spin distributions and matrices for the spin-1/2 case. The spin-1 case is also considered. Moreover, we derive the amplitude density itself from deeper principles involving a real-valued influence function.

This paper outlines a framework that may provide a mathematically rigorous quantum field theory. The framework relies upon the methods of nonstandard analysis. A theory of nonstandard inner product spaces and operators on these spaces is first developed. This theory is then applied to construct nonstandard Fock spaces which extend the standard Fock spaces. Then a rigorous framework for the field operators of quantum field theory is presented. The results are illustrated for the case of Klein-Gordon fields.

Various axiomatic models for unsharp quantum measurements are investigated. These include effect spaces (E-spaces), effect test spaces (E-test spaces), effect algebras, and test groups. It is shown that a test group G is the universal group of an E-test space if and only if G is strongly atomistic. It follows that if G is strongly atomistic, then G is an interpolation group. We then demonstrate that if G is an interpolation group, then G is the universal group of an E-space. (...) Finally, it is shown that an E-space is isomorphic to an E-test space if and only if it is strongly atomistic. (shrink)

This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an (...) order determining set of states. We also consider σ-SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra. (shrink)

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an “effect” and show that observables are related to effect-valued measures. Finally, (...) we define “operational” transformations from M(H) to itself and show that they can be described as a certain combination of effects. (shrink)

Water is the major contributor to the eating and keeping qualities and structure of baked products. Its management and control during preparation, processing, baking, cooling and storage is essential for the optimisation of product quality. This successful and highly practical volume describes in detail the role and control of water in the formation of cake batters, bread, pastry and biscuit doughs, their subsequent processing and the baked product. Now in a fully revised and updated second edition, the book has been (...) expanded and developed through the inclusion of new information and references related to the formation and processing of batters and dough into baked products. The new edition includes a selection of case studies based on practical experience in the manufacture and optimisation of baked products. Each case study, illustrated as appropriate, considers the various roles that water may play in different manufacturing contexts. The book is aimed at food scientists and technologists in bakery companies; ingredient suppliers; flour millers; researchers and students in academic food science departments. (shrink)

El artículo aborda cómo el género oral de las predicaciones agustinianas puede ayudar a la interpretación académica de la teología de san Agustín, de sus ideas, y también puede ayudar a entender mejor a sus oyentes.

The rhetoric of eschatology was formative of early Christian spirituality. Through such discourse the New Testament writers reshaped the community's perception of time and space, and enabled their audiences to “learn Christ.”.

A major shift has taken place since the 1960s concerning disclosure to patients that they have a diagnosis of cancer and that their disease is considered terminal. Full disclosure is now considered the patient's right in the United States. However, there remain many countries in which nondisclosure is still the norm. When patients from those countries are diagnosed with cancer in America, differences in attitudes and expectations can cause conflict and misunderstanding.

In this paper we argue that autobiographical memory can be conceptualized as a mental state resulting from the interplay of a set of psychological capacities?self-reflection, self-agency, self-ownership and personal temporality?that transform a memorial representation into an autobiographical personal experience. We first review evidence from a variety of clinical domains?for example, amnesia, autism, frontal lobe pathology, schizophrenia?showing that breakdowns in any of the proposed components can produce impairments in autobiographical recollection, and conclude that the self-reflection, agency, ownership, and personal temporality are (...) individually necessary and jointly sufficient for autobiographical memorial experience. We then suggest a taxonomy of amnesic disorders derived from consideration of the consequences of breakdown in each of the individual component processes that contribute to the experience of autobiographical recollection. (shrink)

We define qualia space Q to be the space of all possible conscious experience. For simplicity we restrict ourselves to perceptual experience only, though other kinds of experience could also be considered. Qualia space is a highly idealized concept that unifies the perceptual experience of all possible brains. We argue that Q is a closed pointed cone in an infinite-dimensional separable real topological vector space. This quite technical structure can be explained for the most part in a simple, intuitive way. (...) The structure of qualia space allows us to consider and even answer in a precise way such questions as: Is there a continuous path from the sensation of blue to the sensation of pain? Once we fix a desired accuracy of approximation, do there exist finitely many perceptual experiences such that any possible perceptual experience is approximately equal to one of them? What should be meant by ‘fundamentally different’ perceptual experiences? There is the possibility of additional structure, such as a Hilbert space structure on the vector space in which Q is embedded. (shrink)

This paper augments Hailperin's substantial efforts to place Boole's algebra of logic on a solid footing. Namely Horn sentences are used to give a modern formulation of the principle that Boole adopted in 1854 as the foundation for his algebra of logic—we call this principle The Rule of 0 and 1.

There is considerable variability across people in their punitive responses to employee offenses in the workplace. We attempt to explain this variability by positing a novel antecedent of punishment: moral recognition. We find consistent evidence that identifying moral considerations and implications for workplace offenses predicts punitive responses toward employees who commit those offenses. Drawing on functional theoretical accounts of morality and punishment, we posit that people are motivated to punish others to the extent that they believe a moral offense has (...) been committed, because much of what it means to commit a moral offense (as opposed to a non-moral offense) is to act in a way that prevents, or inhibits, cooperative behavior to achieve social goals. Punishment can discourage group members from committing those offenses in the future, thereby regulating behavior in a way that facilitates cooperation and social cohesion. We offer correlational and causal evidence that the link between moral recognition and punishment is explained, in part, by participants’ beliefs that committing these offenses prevents cooperative behavior to achieve organization-related goals. (shrink)

Ethics education has become a priority at many business schools. A common pedagogical strategy in business ethics education has been to encourage students to deliberate and reason about cases and dilemmas. However, relatively little is known about how students actually reason, by default, about business ethics cases and dilemmas. In a large-scale study with undergraduate management students, we investigate how students reason about ethical dilemmas in business. Our results suggest that, after making an initial decision in a dilemma, students rarely (...) changed their minds after deliberating over an extensive set of reasons for both sides of the dilemma. Students evaluated reasons in a way that preferentially supported their initial decisions. This post-hoc evaluation of reasons to preferentially support initial decisions also had implications for decision entrenchment: students actually tended to become more confident in the superiority of their initial decisions after deliberating over the reasons for both sides. We discuss the challenges that our findings pose for teaching business ethics. (shrink)

Fictionalist approaches to ontology have been an accepted part of philosophical methodology for some time now. On a fictionalist view, engaging in discourse that involves apparent reference to a realm of problematic entities is best viewed as engaging in a pretense. Although in reality, the problematic entities do not exist, according to the pretense we engage in when using the discourse, they do exist. In the vocabulary of Burgess and Rosen (1997, p. 6), a nominalist construal of a given discourse (...) is revolutionary just in case it involves a “reconstruction or revision” of the original discourse. Revolutionary approaches are therefore prescriptive. In contrast, a nominalist construal of a given discourse is hermeneutic just in case it is a nominalist construal of a discourse that is put forth as a hypothesis about how the discourse is in fact used; that is, hermeneutic approaches are descriptive. I will adopt Burgess and Rosen’s terminology to describe the two different spirits in which a fictionalist hypothesis in ontology might be advanced. Revolutionary fictionalism would involve admitting that while the problematic discourse does in fact involve literal reference to nonexistent entities, we ought to use the discourse in such a way that the reference is simply within the pretense. The hermeneutic fictionalist, in contrast, reads fictionalism into our actual use of the problematic discourse. According to her, normal use of the problematic discourse involves a pretense. According to the pretense, and only according to the pretense, there exist the objects to which the discourse would commit its users, were no pretense involved. My purpose in this paper is to argue that hermeneutic fictionalism is not a viable strategy in ontology. My argument proceeds in two steps. First, I discuss in detail several problematic consequences of any interesting application of hermeneutic fictionalism. Of course, if there is good evidence that hermeneutic fictionalism is correct in some cases, then some of these drastic consequences would have to be accepted.. (shrink)