Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena (...) and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book. (shrink)

The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, (...) we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Aharonov quantum computational structure. We show that the quotient of this structure is isomorphic to a structure based on a particular set of complex numbers (the closed disc with center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\frac{1}{2},\frac{1}{2})$\end{document} and radius \documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document} ). (shrink)

Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.

This volume includes recent contributions to the philosophy of science from a historical point of view and of the highest topicality: the range of the topics covers all fields in the philosophy of the science provided by authors from around the world focusing on ancient, modern and contemporary periods in the development of the science philosophy. This proceedings is for the scientific community and students at graduate level as well as postdocs in this interdisciplinary field of research.

The term “law” appears in different contexts with different meanings. We are used to speaking of natural laws, legal laws, moral laws, aesthetic laws, historical laws. Such a linguistic convention has represented a constant phenomenon through the history of civilization. Is there any deep common root among all these different uses and meanings?

In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł3 . In spite of the shortness of the paper, all the important points concerning the semantics of Ł3 are already there and can be naturally generalized to the case of a generic number n of truth-values . The conclusion of the article is quite interesting:The present author is of the opinion that three-valued (...) logic has above all theoretical importance as an endeavour to construct a system of non-aristotelian logic. Whether the new system of logic has any practical importance will be seen only when the logical phenomena, especially those in the deductive sciences, are thoroughly examined, and when the consequences of the indeterministic philosophy, which is the metaphysical substratum of the new logic, can be compared with empirical data. (shrink)

The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special (...) quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly “Hilbert-space dependent”. This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point (...) of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures. (shrink)

How are abstract concepts and musical themes recognized on the basis of some previous experience? It is interesting to compare the different behaviors of human and of artificial intelligences with respect to this problem. Generally, a human mind that abstracts a concept (say, table) from a given set of known examples creates a table-Gestalt: a kind of vague and out of focus image that does not fully correspond to a particular table with well determined features. A similar situation arises in (...) the case of musical themes. Can the construction of a gestaltic pattern, which is so natural for human minds, be taught to an intelligent machine? This problem can be successfully discussed in the framework of a quantum approach to pattern recognition and to machine learning. The basic idea is replacing classical data sets with quantum data sets, where either objects or musical themes can be formally represented as pieces of quantum information, involving the uncertainties and the ambiguities that characterize the quantum world. In this framework, the intuitive concept of Gestalt can be simulated by the mathematical concept of positive centroid of a given quantum data set. Accordingly, the crucial problem “how can we classify a new object or a new musical theme (we have listened to) on the basis of a previous experience?” can be dealt with in terms of some special quantum similarity-relations. Although recognition procedures are different for human and for artificial intelligences, there is a common method of “facing the problems” that seems to work in both cases. (shrink)

Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.

The debate about constructivism in physics has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let us (...) briefly mention some important problems that have been debated in the framework of our first class. For instance, the following: to what extent do the undecidability and incompleteness results of classical mathematics affect fragments of physical theories, in such way as to have a “real physical meaning”? are the mathematical arguments that seem to be essential for physics justifiable in the framework of traditional mathematical constructivism?The first question has recently been investigated by Pitowski, Penrose, da Costa, Doria, Mundici, Svozil and others. As expected by most logicians, one can construct undecidable sentences whose physical meaning seems to be hardly questionable. This happens both in classical and in quantum mechanics. (shrink)

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the (...) Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics. (shrink)

The current situation around COVID-19 portrays a threat to us in several ways: It imposes uncertainty, a lack of control and reminds us of our own mortality. People around the world have reacted to these threats in seemingly unrelated ways: From stockpiling yeast and toilet paper to favoring nationalist ideas or endorsing conspiratorial beliefs. According to the General Process Model of Threat and Defense the confrontation with a threat - a discrepant experience - makes humans react with both proximal and (...) distal threat responses. While the proximal response manifests in behavioral inhibition that leads to heightened anxious arousal and vigilance, distal responses seek to lower behavioral inhibition and the associated state of anxiety and vigilance through engaging in distal defenses. In the present research, we propose that the reactions to COVID-19 may represent distal defense strategies to the pandemic (in the form of environmental or group related worldview defenses) and therefore can be explained and forecasted by the model. Thus we hypothesized increased perceived COVID-19 threat perception to lead to a proximal threat response in the form of heightened behavioral inhibition. This, in return, should enhance the use of distal defenses (i.e.: several ingroup biases, system justification and conspiratorial beliefs) overlapping with the reactions observed as a response to COVID-19. This hypothesized mediated effect of increased perceived COVID-19 threat on distal defenses was tested in two pre-registered studies: In Study 1 (N = 358) results showed perceived COVID-19 threat to be related to behavioral inhibition and in turn to be associated with increased distal defenses (i.e., higher entitativity, control restoration motivation, passive party support). In Study 2 (N = 348) we manipulated COVID-19 threat salience and found results suggesting the distal defenses of system justification and conspiratorial beliefs to be mediated by the proximal threat response. The results of the present research hint towards a common mechanism through which the seemingly unrelated reactions to COVID-19 can be explained. The results might help to predict future behavior during the COVID-19 pandemic and design measures to counteract detrimental effects of the pandemic. (shrink)

Drawing on philosophy, law and political science, and on a wealth of practical experience delivering emergency medical services in conflict-ridden settings, Lepora and Goodin untangle the complexities surrounding compromise and complicity.

Chris Letheby’s defence of psychedelic therapy hinges on the premise that psychedelic-facilitated insights about the self are in a better epistemic position than those about the external world. In this commentary, I argue that such a claim is not sufficiently defended. More precisely, I argue that one element is underexplored in Letheby’s otherwise compelling picture: namely, that unlike new beliefs about the external world, beliefs about oneself have the capacity to turn into self-fulfilling prophecies. Recognising the psychedelic experience and the (...) subsequent integration process as opportunities not only to apprehend certain facts about the self but also to actively shape and redetermine those facts is key to understanding the epistemic differences between insights patients have about themselves and about the external world. (shrink)

After initially emerging in China, the coronavirus outbreak has advanced rapidly. The World Health Organization has recently declared it a pandemic, with Europe becoming its new epicentre. Italy has so far been the most severely hit European country and demand for critical care in the northern region currently exceeds its supply. This raises significant ethical concerns, among which is the allocation of scarce resources. Professionals are considering the prioritisation of patients most likely to survive over those with remote chances, and (...) this news has triggered an intense debate about the right of every individual to access healthcare. The proposed analysis suggests that the national emergency framework in which prioritisation criteria are currently enforced should not lead us to perceive scarce resources allocation as something new. From an ethical perspective, the novelty of the current emergency is not grounded in the devastating effects of scarce resources allocation, which is rife in recent and present clinical practice. Rather, it has to do with the extraordinarily high number of people who find themselves personally affected by the implications of scarce resources allocation and who suddenly realise that the principle of ‘equals should be treated equally’ may no longer be applicable. Along with the need to allocate appropriate additional financial resources to support the healthcare system, and thus to mitigate the scarcity of resources, the analysis insists on the relevance of a medical ethics perspective that does not place the burden of care and choice solely on physicians. (shrink)

Boredom, in cinema as well as in our everyday experience, is usually associated with a generalised loss of meaning or interest. Accordingly, boredom is often perceived as that which ought to be avo...

This paper focuses on a specific aspect of political imaginaries: political myth. What are political myths? What role do they play within today commoditised political imaginaries? What are the conditions for setting up a critique of them? We will address these questions, by putting forward a theory of political myth which situates itself between psychoanalysis and political philosophy, in line with the tradition of critical theory that many still associate with the name of the Frankfurt School. We will first discuss (...) the notion of political myth by illustrating the contribution of both disciplines to its understanding and then, through a discussion of the notion of social unconscious, we will apply this analysis to a contemporary example of political myth, that of a clash of civilisations. (shrink)

The exponential accumulation, processing and accrual of big data in healthcare are only possible through an equally rapidly evolving field of big data analytics. The latter offers the capacity to rationalize, understand and use big data to serve many different purposes, from improved services modelling to prediction of treatment outcomes, to greater patient and disease stratification. In the area of infectious diseases, the application of big data analytics has introduced a number of changes in the information accumulation models. These are (...) discussed by comparing the traditional and new models of data accumulation. Big data analytics is fast becoming a crucial component for the modelling of transmission—aiding infection control measures and policies—emergency response analyses required during local or international outbreaks. However, the application of big data analytics in infectious diseases is coupled with a number of ethical impacts. Four key areas are discussed in this paper: automation and algorithmic reliance impacting freedom of choice, big data analytics complexity impacting informed consent, reliance on profiling impacting individual and group identities and justice/fair access and increased surveillance and population intervention capabilities impacting behavioural norms and practices. Furthermore, the extension of big data analytics to include information derived from personal devices, such as mobile phones and wearables as part of infectious disease frameworks in the near future and their potential ethical impacts are discussed. Considered together, the need for a constructive and transparent inclusion of ethical questioning in this rapidly evolving field becomes an increasing necessity in order to provide a moral foundation for the societal acceptance and responsible development of the technological advancement. (shrink)

Medical complicity in torture is prohibited by international law and codes of professional ethics. But in the many countries in which torture is common, doctors frequently are expected to assist unethical acts that they are unable to prevent. Sometimes these doctors face a dilemma: they are asked to provide diagnoses or treatments that respond to genuine health needs but that also make further torture more likely or more effective. The duty to avoid complicity in torture then comes into conflict with (...) the doctor’s duty to care for patients. Sometimes the right thing for a doctor to do requires complicity in torture. Whether this is the case depends on: the expected consequences of the doctor’s actions; the wishes of the patient; and the extent of the doctor’s complicity with wrongdoing. Medical associations can support physicians who face this dilemma while maintaining a commitment to clear principles denouncing torture. (shrink)

The Sārasaṅgaha is a Pāli text of XIIth–XIIIth century by the Sinhalese monk Siddhattha Thera. Its themes include the aspiration to become a Buddha, shrines, meditation, theories on rain, wind, gender and more. The main body consists of citations from the Nikāyas, the Jātakas, the Visuddhimagga and above all, from commentarial literature. By analysing the way the Sārasaṅgaha refers to and establishes a dialogue with the quoted works, this paper promotes a new assessment of the cultural and textual tendencies that (...) influenced the development of Buddhist literature especially in the Middle Ages. In particular, the analysis of this text and the quotations of which it is composed reveals the importance of commentarial literature, a literary genre that only recently has attracted the attention of Pāli scholars. (shrink)

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of (...) functions; finally, we describe the structure of free algebras with one generator in both varieties. (shrink)

We develop an account of how mutually inconsistent models of the same target system can provide coherent information about the system. Our account makes use of ideas from the debate surrounding rob...