Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state.

Recently Flaminio and Montagna (Proceedings of the 5th EUSFLAT Conference, II: 201–206. Ostrava, 2007), (Inter. J. Approx. Reason. 50:138–152, 2009) introduced the notion of a state MV-algebra as an MV-algebra with internal state. We have two kinds: state MV-algebras and state-morphism MV-algebras. These notions were also extended for state BL-algebras in (Soft Comput. doi:10.1007/s00500-010-0571-5). In this paper, we completely describe subdirectly irreducible state-morphism BL-algebras and this generalizes an analogous result for state-morphism MV-algebras presented in (Ann. Pure Appl. Logic 161:161–173, 2009).

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.

We study the idea of implantation of Piron's and Bell's geometrical lemmas for proving some results concerning measures on finite as well as infinite-dimensional Hilbert spaces, including also measures with infinite values. In addition, we present parabola based proofs of weak Piron's geometrical and Bell's lemmas. These approaches will not used directly Gleason's theorem, which is a highly non-trivial result.

We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K.

Pseudo-BCK-algebras are a non-commutative generalization of well-known BCK-algebras. The paper describes a situation when a linearly ordered pseudo-BCK-algebra is an ordinal sum of linearly ordered cone algebras. In addition, we present two identities giving such a possibility of the decomposition and axiomatize the residuation subreducts of representable pseudo-hoops and pseudo-BL-algebras.

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least (...) non-trivial normal ideal. (shrink)

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G 0), where G is an Abelian ℓ-group, G 0 is a subset of the positive cone generating G + (...) such that if u, v ∈ G 0, then 0 ∨ (u - v) ∈ G 0, and morphisms are ℓ-group homomorphisms h: (G, G 0) → (G′,G′0) with f(G 0) ⫅ G′0. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). (shrink)

We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.

An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure.

For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. (...) Finally, the result will be generalized to general inner product spaces. (shrink)

We study positive bilinear forms on a Hilbert space which are not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) σ-complete generalized effect algebras.

We study perfect effect algebras, that is, effect algebras with the Riesz decomposition property where every element belongs either to its radical or to its co-radical. We define perfect effect algebras with principal radical and we show that the category of such effect algebras is categorically equivalent to the category of unital po-groups with interpolation. We introduce an observable on a \-monotone \-complete perfect effect algebra with principal radical and we show that observables are in a one-to-one correspondence with spectral (...) resolutions of observables. (shrink)

The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is countably infinite. In (...) particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H). (shrink)

The perspectives of Ukraine which are outlined by the notion of the “Ukrainian project”, and determined by potential of development of civil society, as congruent with perspectives of steady international development for the sake of collaboration and peace, are examined in the article. Determination of such basic analytical notions as discursive practices of “prevailing” and “understanding” is offered with this purpose. Discourse is considered as reason for choice and giving the advantage to one meaning over the others that is set (...) in the certain modes of signification. Discourse of understanding – is the process of creation of such knowledge, the nominative function of which stops being the function of power, and becomes the instrument of the renewed perception and understanding at new level of communicative space. As discursive reality is reflected not only on the methods of thinking, but also on the practical behaviour of people, we have warrants to speak about its ethical conditionality and the corresponding discursive‐ethical practices of “freedom and authenticity”, “paternalism and clientism” and “nihilism and anarchy”. Last two discursive-ethical practices are examined as obstacles on the way to realization of the “Ukrainian project” in relation to itsdemocratic development in direction to the civilization values common with the European Union. (shrink)

We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states.

We discuss the interrelations between BCK-algebras and posets with difference. Applications are given to bounded commutative BCK-algebras, difference posets, MV-algebras, quantum MV-algebras and orthoalgebras.

Comment devient-on philosophe? Par quel sursaut un Aristoclès se fait-il Platon, jusqu'à s'imposer dans la liste des " auteurs philo " Il faut enquêter, non pas sur la vie privée, mais sur la vie intime : rumination intellectuelle, ton sur lequel on parle, motivations amoureuses... Ce qui fait un philosophe, c'est un immense travail sur soi, et la rencontre d'autres philosophes, vivants, de leurs problématiques. Mémoire sémantique + obsession métaphysique, voilà le code génétique du philosophe. Il débute par un attentat (...) religieux, puisqu'il commence sa carrière en niant tel ou tel sacré. Bien sûr, il vaut mieux être mâle, communiquer par les livres adopter la langue dominante, écrire quand on est célibataire. Comment gagner sa vie? Pas forcément en étant enseignant, comme c'est le cas aujourd'hui. Le profil du philosophe nous le révèle orphelin, vivant à l'étranger, souvent laid, jamais fou, et serial thinker, prêt à changer de philosophie pourvu qu'il reste, lui, à menacer le monde donnera ou donnera pas du sens à notre vie? Le philosophe est l'être inquiet qui pense inquiéter l'Être par deux trois mots bien aiguisés. (shrink)

Dopo la Grande Guerra e la Rivoluzione d’Ottobre, l’Europa e la Russia vissero una intensa crisi. Il saggio ricostruisce la dimensione internazionale della situazione in Italia tra il 1919 e 1922. Esso si concentra in particolare su due “futuristi di sinistra”, Vinicio Paladini e Ivo Pannaggi, influenzati da Alexandr Bogdanov e Anatolij Lunačarskij, il futuro Commissario del Popolo per l’Istruzione. Esso si concentra anche sulla rivista “Vešč/Gegenstand/Objet", fondata da El Lissitzky e Ilya Ehrenburg a Berlino nel 1922, i suoi (...) legami con il Purismo francese e Pannaggi. (shrink)

While there are numerous doubts, controversies and lack of consensus on alternative definitions of human death, it is argued that it is more ethical to allow people to choose either cessation of cardio-respiratory function or loss of entire brain function as the definition of death based on their own views. This paper presents the law of organ transplantation in Japan, which allows people to decide whether brain death can be used to determine their death in agreement with their family. Arguably, (...) Japan could become a unique example of individual choice in the definition of death if the law is revised to allow individuals choose definition of death independently of their family. It suggests that such an approach is one of the reasonable policy options a country can adopt for legislation on issues related to the definition of death. (shrink)

How (Not) to Be Secular is what Jamie Smith calls "your hitchhiker's guide to the present" -- it is both a reading guide to Charles Taylor's monumental work A Secular Age and philosophical guidance on how we might learn to live in our times. Taylor's landmark book A Secular Age (2007) provides a monumental, incisive analysis of what it means to live in the post-Christian present -- a pluralist world of competing beliefs and growing unbelief. Jamie Smith's book is a (...) compact field guide to Taylor's insightful study of the secular, making that very significant but daunting work accessible to a wide array of readers. Even more, though, Smith's How (Not) to Be Secular is a practical philosophical guidebook, a kind of how-to manual on how to live in our secular age. It ultimately offers us an adventure in self-understanding and maps out a way to get our bearings in today's secular culture, no matter who "we" are -- whether believers or skeptics, devout or doubting, self-assured or puzzled and confused. This is a book for any thinking person to chew on. (shrink)

Extraterrestrial Altruism examines a basic assumption of the Search for Extraterrestrial Intelligence (SETI): that extraterrestrials will be transmitting messages to us for our benefit. This question of whether extraterrestrials will be altruistic has become increasingly important in recent years as SETI scientists have begun contemplating transmissions from Earth to make contact. Technological civilizations that transmit signals for the benefit of others, but with no immediate gain for themselves, certainly seem to be altruistic. But does this make biological sense? Should we (...) expect altruism to evolve throughout the cosmos, or is this only wishful thinking? Is it dangerous to send messages to other worlds, as Stephen Hawking has suggested, or might humankind benefit from an exchange with intelligence elsewhere in the galaxy? Would extraterrestrial societies be based on different ethical principles, or would we see commonalities with Earthly notions of morality? Extraterrestrial Altruism explores these and related questions about the motivations of civilizations beyond Earth, providing new insights that are critical for SETI. Chapters are authored by leading scholars from diverse disciplines—anthropology, astronomy, biology, chemistry, computer science, cosmology, engineering, history of science, law, philosophy, psychology, public policy, and sociology. The book is carefully edited by Douglas Vakoch, Director of Interstellar Message Composition at the SETI Institute and professor of clinical psychology at the California Institute of Integral Studies. The Foreword is by Frank Drake. This interdisciplinary book will benefit everybody trying to understand whether evolution and ethics are unique to Earth, or whether they are built into the fabric of the universe. (shrink)

Introduction: Conversion and the practice of transformation -- The philosophical structure of Jonathan Edwards's religious affections -- Habit, habit change, and conversion in C.S. Peirce -- Reconstructing faith : religious overcoming in Dewey's pragmatism -- Transforming obligation in William James -- Dwelling in absence: the reflective origin of conversion -- Creative transformation : the work of conversion -- The evasion of conversion in recent American philosophy.

Ludwig Wittgenstein (1889-1951) was an extraordinarily original thinker, whose influence on twentieth-century thinking far outside the bounds of philosophy alone. In this engaging Introduction, A.C. Grayling makes Wittgenstein's thought accessible to the general reader by explaining the nature and impact of Wittgenstein's views. He describes both his early and later philosophy, the differences and connections between them, and gives a fresh assessment of Wittgenstein's continuing influence on contemporary thought.

Background: The magnitude of bullying and harassment among psychiatrists is reportedly high, yet no peer-review published studies addressing this issue could be found. Therefore, it was decided to conduct a pilot study to assess the degree of the problem, the types of bullying/harassment and to provide some insights into the situation.Methods and Principal Findings: Following multiple focus group meetings, a yes/no response type questionnaire was developed to assess the degree and type of bullying and harassment experienced by psychiatrists. Over a (...) 3-month period the questionnaire was administered to a random sample of 60 psychiatrists. 57 out of the 60 psychiatrists reported harassment and bullying. Frequencies of the following response variables are presented in descending order: rumours 40% ; defamation 20% ; passing remarks 20% ; false accusations 15% ; threats 13.3% ; verbal abuse 13.3% ; unjustified complaints 13.3% ; promotion blocked 13.3% ; humiliation 13% ; bad reference given 10% ; credentials questioned 8.3% ; physical attacks 5% ; termination 5% ; derogatory remarks 1.7% and 1.7% were subjected to personal work. As a result of being subjected to harassment, 66.7% of the psychiatrists did not take any action, whereas 33.3% confronted the person they believed responsible. Asked whether the bullying and harassment caused distress, 18.3% of the psychiatrists did not report any effect, 30% reported mild distress, 40% moderate distress and severe distress was reported by 11.7%.Conclusions: It was concluded that the magnitude of bullying and harassment among psychiatrists may be quite high, as evidenced by this pilot study. There is a need for extensive systematic studies on this subject and to establish strategies to prevent and address this issue at a national and regulatory level. (shrink)