In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an agent in order to compute measurement outcomes, the objectivist interpretation understands quantum probability as providing reliable information of a real state of affairs. After discussing these different viewpoints we propose a particular objectivist interpretation grounded on the idea that the Born rule provides information about an (...) intensive realm of reality. We then turn our attention to the way in which the subjectivist interpretation of probability is presently applied within both quantum computation and quantum computational logic. Taking as a standpoint our proposed intensive account of quantum probability we discuss the possibilities and advantages it might open for the modeling and development of both quantum computation and quantum computational logic. (shrink)

Quantum Logic in Historical and Philosophical Perspective Quantum Logic was developed as an attempt to construct a propositional structure that would allow for describing the events of interest in Quantum Mechanics. QL replaced the Boolean structure, which, although suitable for the discourse of classical physics, was inadequate for representing the atomic realm. The … Continue reading Quantum Logic →.

In Aristotelian logic, categorical propositions are divided in Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative. Possible relations between two of the mentioned type of propositions are encoded in the square of opposition. The square expresses the essential properties of monadic first order quantification which, in an algebraic approach, may be represented taking into account monadic Boolean algebras. More precisely, quantifiers are considered as modal operators acting on a Boolean algebra and the square of opposition is represented by relations (...) between certain terms of the language in which the algebraic structure is formulated. This representation is sometimes called the modal square of opposition. Several generalizations of the monadic first order logic can be obtained by changing the underlying Boolean structure by another one giving rise to new possible interpretations of the square. (shrink)

In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert-style calculus is introduced obtaining a strong completeness theorem.

In the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$ ⋁ κ -complete Heyting algebras or Heyting $$\kappa $$ κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$ κ -frames, an equational type completeness theorem related to the $$\langle \bigvee, \wedge, \rightarrow, 0 \rangle $$ ⟨ ⋁, ∧, →, 0 ⟩ -structure of frames is also obtained.

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.

In this paper we investigate a categorical equivalence between square root qMV-algehras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.

Objective Gather information from physicians about factors contributing to unnecessary noninvasive imaging and impact of possible solutions. Methods Qualitative study of 14 physicians using a phenomenological approach and the Theoretical Domains Framework. Results Most participants self-reported that >10% of the imaging tests they order are unnecessary. External sources of pressure included: peer-review, patient demands, nursing expectations, specialist requests, as well as prior experience with patient advocates, and the compensation and pension system. Internal sources of pressure included reliance on anecdote, self-doubt (...) about diagnoses, and fear of missing a diagnosis and of professional liability. Participants expressed both optimism and concern about potential solutions, such as adopting decision support software. Conclusion Physicians are under pressure from multiple sources to order unnecessary imaging. Peer review, nursing expectations, and perceptions about Veteran compensation and pension are newly reported contributing factors. (shrink)

We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of (...) non-trivial correlations between the different species involved, opening the door to a new way of harnessing these physical resources for solving pattern recognition problems. Finally, we present some examples and discuss the computational complexity of the quantum pattern recognition problem, showing that the most important quantum computation algorithms can be described as non-Kolmogorovian pattern recognition problems. (shrink)

In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.

Terence Irwin's edition of the Nicomachean Ethics offers more aids to the reader than are found in any modern English translation. It includes an Introduction, headings to help the reader follow the argument, explanatory notes on difficult or important passages, and a full glossary explaining Aristotle's technical terms. The Third Edition offers additional revisions of the translation as well as revised and expanded versions of the notes, glossary, and Introduction. Also new is an appendix featuring translated selections from related texts (...) of Aristotle. (shrink)

In this paper we attempt to physically interpret the Modal Kochen–Specker theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible (...) realms. (shrink)

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].

This volume offers a collection of in-depth explorations of pragmatism as a framework for discussions in philosophy of science and metaphysics. Each chapter involves explicit reflection on what it means to be pragmatist, and how to use pragmatism as a guiding framework in addressing topics such as realism, unification, fundamentality, truth, laws, reduction, and more. -/- .

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.

كتاب بحصي يتناول الصراع بين الصوفية والسلفية ويتناول قصة حياة الحلاج وابن الفارض والسهروردي ودواوينهم ويتناول الحب الإلهي عند الصوفية.

An English language translation accompanies the original Greek text of Aristotle's book about the nature of the state, constitutions, revolutions, democracy, and oligarchy.

"First published by Oxford University Press, 1916."--Title page verso.

This is the first complete, one-volume English translation of the ancient Chinese text Xunzi, one of the most extensive, sophisticated, and elegant works in the tradition of Confucian thought. Through essays, poetry, dialogues, and anecdotes, the Xunzi articulates a Confucian perspective on ethics, politics, warfare, language, psychology, human nature, ritual, and music, among other topics. Aimed at general readers and students of Chinese thought, Eric Hutton’s translation makes the full text of this important work more accessible in English than ever (...) before. Named for its purported author, the Xunzi has long been neglected compared to works such as the Analects of Confucius and the Mencius. Yet interest in the Xunzi has grown in recent decades, and the text presents a much more systematic vision of the Confucian ideal than the fragmented sayings of Confucius and Mencius. In one famous, explicit contrast to them, the Xunzi argues that human nature is bad. However, it also allows that people can become good through rituals and institutions established by earlier sages. Indeed, the main purpose of the Xunzi is to urge people to become as good as possible, both for their own sakes and for the sake of peace and order in the world. In this edition, key terms are consistently translated to aid understanding and line numbers are provided for easy reference. Other features include a concise introduction, a timeline of early Chinese history, a list of important names and terms, cross-references, brief explanatory notes, a bibliography, and an index. (shrink)

This incisive book deals with the use of the criminal law to enforce morality, in particular sexual morality, a subject of particular interest and importance since the publication of the Wolfenden Report in 1957. Professor Hart first considers John Stuart Mill's famous declaration: "The only purpose for which power can be rightfully exercised over any member of a civilized community is to prevent harm to others." During the last hundred years this doctrine has twice been sharply challenged by two great (...) lawyers: Sir James Fitzjames Stephen, the great Victorian judge and historian of the common law, and Lord Devlin, who both argue that the use of the criminal law to enforce morality is justified. The author examines their arguments in some detail, and sets out to demonstrate that they fail to recognize distinction of vital importance for legal and political theory, and that they espouse a conception of the function of legal punishment that few would now share. (shrink)

A classic exposition of Kant's ethical thought.

Engelhardt invites readers to understand what it means to live in a world after God, where questions of sin and virtue have been replaced with life-and-death-style choices. After God provides a dark prophetic vision. But there is still hope. As Engelhardt argues, In this culture, children now grow up apart from and defended against a recognition of the God Who lives. They are nurtured in a social fabric that is structured so as to avoid a recognition of, much less an (...) encounter with, God. Nevertheless... a traditional Christianity has endured, even though its morality and bioethics have become ever more strongly counter-cultural. The source of this traditional Christian otherness over against the surrounding post-theistic culture lies in the origins of Christianity itself, in the Christianity of the Apostles and the Fathers, namely, in Orthodox Christianity. Against the tenor of the times, disregarding the animus to set traditional Christianity aside, and despite heretics prominent within its fold, Orthodox Christianity remains a light in a world after God. --! From back cover. (shrink)

The paper defends the position that phenomenological interviews can provide a rich source of knowledge and that they are in no principled way less reliable or less valid than quantitative or experimental methods in general. It responds to several skeptic objections such as those raised against introspection, those targeting the unreliability of episodic memory, and those claiming that interviews cannot address the psychological, cognitive and biological correlates of experience. It argues that the skeptic must either heed the methodological and epistemological (...) justification of the phenomenological interview provided, or embrace a more fundamental skepticism, a “deep mistrust”, in which scientific discourse can have no recourse to conscious processes as explananda, with ensuing dire consequences for our conception of science. (shrink)