We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy; strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a (...) natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass, et al. (shrink)

Amid a global zeitgeist of impending catastrophe, this book explores the culture of fear so prevalent in today's politics, economic climate, and religious extremism.

A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.

Brain-Computer Interface is a set of technologies that are of increasing interest to researchers. BCI has been proposed as assistive technology for individuals who are non-communicative or paralyzed, such as those with amyotrophic lateral sclerosis or spinal cord injury. The technology has also been suggested for enhancement and entertainment uses, and there are companies currently marketing BCI devices for those purposes as well as health-related purposes. The unprecedented direct connection created by BCI between human brains and computer hardware raises various (...) ethical, social, and legal challenges that merit further examination and discussion. To identify and characterize the key issues associated with BCI use, we performed a scoping review of biomedical ethics literature, analyzing the ethics concerns cited across multiple disciplines, including philosophy and medicine. Based on this investigation, we report that BCI research and its potential translation to therapeutic intervention generate significant ethical, legal, and social concerns, notably with regards to personhood, stigma, autonomy, privacy, research ethics, safety, responsibility, and justice. Our review of the literature determined, furthermore, that while these issues have been enumerated extensively, few concrete recommendations have been expressed. We conclude that future research should focus on remedying a lack of practical solutions to the ethical challenges of BCI, alongside the collection of empirical data on the perspectives of the public, BCI users, and BCI researchers. (shrink)

For a century the Bahá’í Faith has been classified, within the German academy, as a world religion. This article highlights the major historical milestones in this process of recognition. The process was initiated on the eve of the First World War by the two Jewish Germanophone orientalists Goldziher and Vambery. In the inter-war period, the categorization of this faith as a world religion – rather than a sect of Islam, as it had once been viewed – was further propelled by (...) academics outside the field of theology and religious studies, such as the natural scientist Auguste Forel. It was only after the catastrophic experience of World War II, a period when the German Bahá’í community evinced a spirit of resilience in the face of Nazi oppression, that scholars in the field of Christian theology and religious studies, such as Heiler, Mensching and Benz, who represented the school of Religionswissenschaft des Verstehens, began to adopt the classification of the Bahá’ís as new world religion. (shrink)

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...) is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. (shrink)

Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the (...) underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e., properties which can be determined to hold of a process on the basis of a finite amount of information about its execution.These ideas lead to the following programme. A metalanguage is introduced, comprising• types = universes of discourse for various computational situations;• terms = PROGRAMS = syntactic intensions for models or points. A standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms. The metalanguage is also given a logical interpretation, in which types are interpreted as propositional theories and terms are interpreted via a program logic, which axiomatises the properties they satisfy. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our metalanguage, we can turn the handle to obtain a logic for that situation. (shrink)

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.

We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

Throughout the critical period Kant enigmatically insists that reason is a ‘unity’, thereby suggesting that both our theoretical and practical endeavors are grounded in one and the same rational capacity. How Kant's unity thesis ought to be interpreted and whether it can be substantiated remain sources of controversy in the literature. According to the strong reading of this claim, reason is a ‘unity’ because all our reasoning, including our theoretical reasoning, functions practically. Although several prominent commentators endorse this view, it (...) is widely thought to lack exegetical support. This paper seeks to strengthen the case for this reading by showing how theoretical reason's positive function, as Kant presents it in the Appendix to the Transcendental Dialectic, may be construed as fundamentally practical. I argue that reason's supreme regulative principle ought to be understood as a categorical practical imperative. This interpretation, I suggest, resolves the apparent inconsistencies that blight Kant's account of the principle in the Appendix, while bringing greater overall coherence to his account of theoretical reason's regulative function. (shrink)

ABSTRACTSharing experiences with others, even without communication, can amplify those experiences. We investigated whether shared stressful experiences amplify. Participants completed the Cold Pre...

Third Line is an installation of video projections and selected artefacts presented at the 2014 International Žižek Studies Conference: Parallax Future in Art and Design, Ideology, and Philosophy, with the support of the Ontario Arts Council. Third Line represents a self-referential and speculative study of haiku structure, in conjunction with the idea of optical interference and parallax. The title refers to Žižek’s explanation of the haiku function: the third line of haiku stands for the momentary event where reality loses its (...) substantial mass. The objective was to create a visual experience that affiliates the haiku structure with an experiential system of visual perception. We designed a dual, parallax video projection system, with one facet of the screen revealing a sequence of haiku text – metaphrasms systematically extracted from Žižek’s books – as the other side showed a video of ambient, material dissolution. The installation also featured a tableau of collected objects, referencing the project’s material development and ideological framework. (shrink)

Levinas's project throughout Totality and Infinity and in his earlier works Existence and Existents and Time and the Other is to situate the primacy of the ethical as foundational first philosophy. For Levinas, myth is intimately connected to being, the being before reflection and thought. The entering into reflection and thought Levinas terms transcendence, the epoché, or first ethical gesture. In order to situate his ethics, Levinas turns to the Cartesian notion of infinity: the idea of infinity as an overflowing (...) presence, the container capable of containing more than it can draw from itself, from its own being.1 This idea of infinity is grounded in an experience of the Other as primal.2 The presence of a face... (shrink)

Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of (...) situations. There is a single clear conceptual principle, based on purely logical consistency conditions, which underlies our notion of logical Bell inequalities. We show that in a precise sense, all Bell inequalities can be taken to be of this form. Our approach is very general. It applies directly to any family of sets of commuting observables. Thus it covers not only the n-partite scenarios to which Bell inequalities are standardly applied, but also Kochen-Specker configurations, and many other examples. There is much current work on experimental tests for contextuality. Our approach directly yields, in a systematic fashion, testable inequalities for a very general notion of contextuality. There has been much work on obtaining proofs of Bell's theorem “without inequalities” or “without probabilities.” These proofs are seen as being in a sense more definitive and logically robust than the inequality-based proofs. On the hand, they lack the fault-tolerant aspect of inequalities. Our approach reconciles these aspects, and in fact shows how the logical robustness can be converted into systematic, general derivations of inequalities with provable violations. Moreover, the kind of strong non-locality or contextuality exhibited by the GHZ argument or by Kochen-Specker configurations can be shown to lead to maximal violations of the corresponding logical Bell inequalities. Thus the qualitative and the quantitative aspects are combined harmoniously. (shrink)

Ectogenesis, or “artificial womb technology,” has been heralded by some, such as prominent feminist Shulamith Firestone, as a way to liberate women. In this chapter, we challenge this view by offering an alternative analysis of the technology as relying upon and perpetuating a problematic model of pregnancy which, rather than liberating women, serves to devalue them. We look to metaphysics as the abstract study of reality to elucidate how the entities in a pregnancy are related to one another. We consider (...) two models of the metaphysics of pregnancy: (1) the Parthood Model, whereby the fetus is a part of what/who gestates it; and (2) and the Fetal Container Model, whereby the gestator is a container for the fetus. We suggest that under the assumption of the Fetal Container Model, we are more likely to think that any container will suffice for gestation, even an artificial one. In contrast, under the assumption of the Parthood Model, we are less likely to treat the gestator as interchangeable or replaceable, given the parthood relationship between gestator and fetus. This chapter argues that ectogenesis is conceptually linked to the Fetal Container Model and advocates a more cautious approach in promoting ectogenesis as a tool for women’s liberation. (shrink)

Through myths that pattern and repeat we figure the world to ourselves. The desire to be done with myth, to surpass mythic thinking in favor of a “more” rational way of thinking, is but one way of perpetrating violence in the guise of similitude. The rejection of muthos by logos is itself a form of violence, with significant ramifications. The following analysis will explore the work of Luce Irigaray’s Speculum of the Other Woman, and Jean-Luc Nancy’s Inoperative Community, focusing on (...) the ways in which myth becomes mythology, and the inescapable question of violence that attends this operation. This paper, although touching upon the matter, is not an attempt to answer the larger question of what myth is. The scope of this analysis is constrained to a discussion of both Nancy and Irigaray’s understanding of myth as foundational, as well as interrogating the nature of the violence of representation. I will briefly touch upon the long and elaborate conversation surrounding the muthos–logos divide. (shrink)

A structure has a automatic presentationif the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.

A short scientific biography emphasising the main phases of Abramsky’s research: duality theory and domains in logical form, game semantics, categorical quantum mechanics, the sheaf-theoretic approach to contextuality, and game comonads and a structural view of resources and descriptive complexity.

Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding a semantically (...) motivated model satisfying this principle remained an open problem.In the present paper, we construct a categorical model of polymorphism, based on game semantics, which contains a large collection of generic types. This model builds on two novel constructions:•A direct interpretation of variable types as games, with a natural notion of substitution of games. This allows moves in games A[T] to be decomposed into the generic part from A, and the part pertaining to the instance T. This leads to a simple and natural notion of generic strategy.•A “relative polymorphic product” which expresses quantification over the type variable Xi in the variable type A with respect to a “universe” which is explicitly given as an additional parameter B. We then solve a recursive equation involving this relative product to obtain a universe in a suitably “absolute” sense.Full Completeness for ML types is proved for this model. (shrink)

We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models over them which are fully complete, inter alia, w.r.t. the following languages and theories: the fragment of System F consisting of ML-types, (...) the maximal theory on the simply typed λ-calculus with finitely many ground constants, and the maximal theory on an infinitary version of this latter calculus. (shrink)

In this article I undertake an analysis of erotic sexual intercourse - commonly, and more accurately, designated as love-making - in the spirit of Durkheim's social analysis of religion. Thus, based on a phenomenological semiotic analysis of the peculiar things we do and feel in the course of making love, I propose, first, to uncover the implicit `logic' that generates and governs these distinctly sociable doings and sociable feelings. Second, I proceed to suggest that the sameself logic, albeit in an (...) attenuated version, also generates and governs the broad class of `social occasions proper', and that this homology calls for gathering erotic and social occasions under one and the same rubric, which I propose to call the `socio-erotic' (since the term `social' has been denatured through overuse). Third, I conclude with a discussion of how socio-erotic domains fit into a larger world structured and governed mainly by interest-driven and power-driven conflictual fields. (shrink)

Los desacuerdos acerca de la ontología científica han sido frecuentemente reconstruidos como el resultado de una disputa entre stances epistémicas rivales. En el presente trabajo, (i) caracterizamos algunos de estos desacuerdos como desacuerdos profundos. Además, (ii) mostramos que los desacuerdos profundos sobre ontología científica pueden surgir no solo de la adopción de diferentes stances epistémicas, sino entre posiciones que se encuadran dentro de una misma stance. El desarrollo de ese punto nos permite, a su vez, establecer una distinción entre tipos (...) de desacuerdos profundos y explorar la posibilidad de que existan diferencias de grado entre ellos. (shrink)

We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a 'big toy model', in which both quantum and classical systems can be faithfully represented—as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can (...) be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems—the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hubert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness. (shrink)

Catherine Elgin proposes a novel principle for identifying epistemic virtue. Based loosely on Kant’s Categorical Imperative, it identifies autonomy as our fundamental epistemic responsibility, and defines the epistemic virtues as those traits of character needed to exercise epistemic autonomy. I argue that Elgin’s principle fails as a criterion of epistemic virtue because the instrumental conception of autonomy on which it relies leads to an untenable relativism. Despite this, I suggest that autonomy may yet furnish a plausible criterion for epistemic virtue, (...) provided we construe autonomy as Kant does, as grounded in categorical rather than instrumental reason. (shrink)