Formal concept analysis and structures underlying quantum logics

A Hilbert space $H$ induces a formal context, the Hilbert formal context $\overline H$, whose associated concept lattice is isomorphic to the lattice of closed subspaces of $H$. This set of closed subspaces, denoted $\mathcal C(H)$, is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of $\text{ChuCors}_{\mathcal H}$ of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A New Linear Logic for Deadlock-Free Session-Typed Processes

The π -calculus, viewed as a core concurrent programming language, has been used as the target of much research on type systems for concurrency. In this paper we propose a new type system for deadlock-free session-typed π -calculus processes, by integrating two separate lines of work. The first is the propositions-as-types approach by Caires and Pfenning, which provides a linear logic foundation for session types and guarantees deadlock-freedom by forbidding cyclic process connections. The second is Kobayashi’s approach in which types are annotated with priorities so that the type system can check whether or not processes contain genuine cyclic dependencies between communication operations. We combine these two techniques for the first time, and define a new and more expressive variant of classical linear logic with a proof assignment that gives a session type system with Kobayashi-style priorities. This can be seen in three ways: (i) as a new linear logic in which cyclic structures can be derived and a CYCLE -elimination theorem generalises CUT -elimination; (ii) as a logically-based session type system, which is more expressive than Caires and Pfenning’s; (iii) as a logical foundation for Kobayashi’s system, bringing it into the sphere of the propositions-as-types paradigm

Conway games, algebraically and coalgebraically

Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning strategies, we focus on non-losing strategies. Hypergames are a fruitful metaphor for non-terminating processes, Conway's sum being similar to shuffling. We develop a theory of hypergames, which extends in a non-trivial way Conway's theory; in particular, we generalize Conway's results on game determinacy and characterization of strategies. Hypergames have a rather interesting theory, already in the case of impartial hypergames, for which we give a compositional semantics, in terms of a generalized Grundy-Sprague function and a system of generalized Nim games. Equivalences and congruences on games and hypergames are discussed. We indicate a number of intriguing directions for future work. We briefly compare hypergames with other notions of games used in computer science.Comment: 30 page

Development and Validation of the False Disorder Score: The Focal Scale of the Inventory of Problems

This article introduces the Inventory of Problems (IOP)-a new, computerized, 181-item tool designed to discriminate bona fide from feigned mental illness and cognitive impairment-and presents the development and validation of its focal, feigning scale, the False Disorder Score (IOP-FDS). The initial sample included (a) 211 patients and 64 offenders who took the IOP under standard conditions, and (b) 210 community volunteers and 64 offenders who feigned mental illness. We split this sample into three subsamples. The first

Process types as a descriptive tool for interaction

We demonstrate a tight relationship between linearly typed π-calculi and typed λ-calculi by giving a type-preserving translation from the call-by-value λµ-calculus into a typed π-calculus. The λµ-calculus has a particularly simple representation as typed mobile processes. The target calculus is a simple variant of the linear π-calculus. We establish full abstraction up to maximally consistent observational congruences in source and target calculi using techniques from games semantics and process calculi

Immune Dysregulation and Self-Reactivity in Schizophrenia: Do Some Cases of Schizophrenia Have an Autoimmune Basis?

Schizophrenia affects 1% of the world's population, but its cause remains obscure. Numerous theories have been proposed regarding the cause of schizophrenia, ranging from developmental or neurodegenerative processes or neurotransmitter abnormalities to infectious or autoimmune processes. In this review, findings suggestive of immune dysregulation and reactivity to self in patients with schizophrenia are examined with reference to criteria for defining whether or not a human disease is autoimmune in origin. Associations with other autoimmune diseases and particular MHC haplotypes, increased serum levels of autoantibodies, and in vivo and in vitro replication of some of the functional and ultrastructural abnormalities of schizophrenia by transfer of autoantibodies from the sera of patients with schizophrenia suggest that, in some patients at least, autoimmune mechanisms could play a role in the development of disease. Recent findings regarding specific autoimmune responses directed against neurotransmitter receptors in the brain in patients with schizophrenia will also be reviewed

Male and female physical intimate partner violence and socioeconomic position: a cross-sectional international multicentre study in Europe

Objectives: This work explores the association between socioeconomic position (SEP) and intimate partner violence (IPV) considering the perspectives of men and women as victims, perpetrators and as both (bidirectional). Study Design: Cross-sectional international multicentre study. Methods: A sample of 3496 men and women, (aged 18-64 years), randomly selected from the general population of residents from six European cities was assessed: Athens, Budapest, London, Östersund, Porto and Stuttgart. Their education (primary, secondary and university), occupation (upper white-collar, lower white-collar and blue collar) and unemployment duration (never, ≤12 months and >12 months) were considered as SEP indicators and physical IPV was measured with the Revised Conflict Tactics Scales. Results: Past year physical IPV was declared by 17.7% of women (3.5% victims, 4.2% perpetrators and 10.0% bidirectional) and 19.8% of men (4.1% victims, 3.8% perpetrators and 11.9% bidirectional). Low educational level (primary vs. university) was associated with female victimization (adjusted Odds Ratio, 95% confidence interval: 3.2, 1.3-8.0) and with female bidirectional IPV (4.1, 2.4-7.1). Blue collar occupation (vs. upper white) was associated with female victimization (2.1, 1.1-4.0), female perpetration (3.0, 1.3-6.8) and female bidirectional IPV (4.0, 2.3-7.0). Unemployment duration was associated with male perpetration (> 12 months of unemployment vs. never unemployed: 3.8, 1.7-8.7) and with bidirectional IPV in both sex (women: 1.8, 1.2-2.7; men: 1.7, 1.0-2.8). Conclusions: In these European centers, physical IPV was associated with a disadvantaged socioeconomic position. A consistent socioeconomic gradient was observed in female bidirectional involvement, but victims or perpetrators-only presented gender specificities according to levels of education, occupation differentiation and unemployment duration potentially useful for designing interventions

Constructive Hybrid Games

Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where proofs that a player can win the game correspond to computable winning strategies. This is the logical foundation for synthesis of correct control and monitoring code for safety-critical cyber-physical systems. Our contributions include novel static and dynamic semantics as well as soundness and consistency.Comment: 60 pages, preprint, under revie

Models of a Non-Associative Composition

International audienceWe characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as a reference to Jean-Louis Loday's duplicial algebras. The main result is a reflection Adj→Dupl where Dupl is a category of duploids and duploid functors, and Adj is the category of adjunctions and pseudo maps of adjunctions. The result suggests that the various biases in denotational semantics: indirect, call-by-value, call-by-name... are a way of hiding the fact that composition is not always associative.Nous caractérisons l'ordre d'évaluation polarisé à travers une structure catégorielle dont l'hypothèse que la composition est associative est relâchée. Duploïde est le nom de la structure, par référence aux algèbres dupliciales de Loday. Le résultat principal est une réflection Adj→Dupl où Dupl est une catégorie des duploïdes et des foncteurs de duploïdes, et Adj est la catégorie des adjonctions et des pseudo-morphismes d'adjonctions. Le résultat suggère que les biais des sémantiques dénotationnelles: indirectes, en appel par valeur, en appel par nom... sont des façons de cacher le fait que la composition n'est pas toujours associative

A Pragmatic, Scalable Approach to Correct-by-Construction Process Composition Using Classical Linear Logic Inference

The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process composition, with guaranteed deadlock freedom, systematic resource accounting, and concurrent execution. We introduce algorithms to automate the necessary inference steps for binary compositions of processes in parallel, conditionally, and in sequence. We combine decision procedures and heuristics to achieve intuitive and practically useful compositions in an applied setting.Comment: Post-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326). arXiv admin note: substantial text overlap with arXiv:1803.0261