The Structure of First-Order Causality

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order propositional logic. One of the main difficulties that has to be faced during the elaboration of this kind of semantics is to characterize definable strategies, that is strategies which actually behave like a proof. This is usually done by restricting the model to strategies satisfying subtle combinatorial conditions, whose preservation under composition is often difficult to show. Here, we present an original methodology to achieve this task, which requires to combine advanced tools from game semantics, rewriting theory and categorical algebra. We introduce a diagrammatic presentation of the monoidal category of definable strategies of our model, by the means of generators and relations: those strategies can be generated from a finite set of atomic strategies and the equality between strategies admits a finite axiomatization, this equational structure corresponding to a polarized variation of the notion of bialgebra. This work thus bridges algebra and denotational semantics in order to reveal the structure of dependencies induced by first-order quantifiers, and lays the foundations for a mechanized analysis of causality in programming languages

Full abstraction for probabilistic PCF

We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-by-name, we allow a call-by-value evaluation for ground type arguments in order to provide the language with a suitable algorithmic expressiveness. We describe a denotational semantics based on probabilistic coherence spaces, a model of classical Linear Logic developed in previous works. We prove an adequacy and an equational full abstraction theorem showing that equality in the model coincides with a natural notion of observational equivalence

Measurable Cones and Stable, Measurable Functions

We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a call-by-name operational semantics and give some examples of its denotations

Stream Associative Nets and Lambda-mu-calculus

$\Lambda\mu$-calculus has been built as an untyped extension of Parigot's $\lambda\mu$-calculus in order to recover Böhm theorem which was known to fail in $\lambda\mu$-calculus. An essential computational feature of $\Lambda\mu$-calculus for separation to hold is the unrestricted use of abstractions over continuations that provides the calculus with a construction of streams. Based on the Curry-Howard paradigm Laurent has defined a translation of $\Lambda\mu$-calculus in polarized proof-nets. Unfortunately, this translation cannot be immediately extended to $\Lambda\mu$-calculus: the type system on which it is based freezes \Lm-calculus's stream mechanism. We introduce \emph{stream associative nets (SANE)}, a notion of nets which is between Laurent's polarized proof-nets and the usual linear logic proof-nets. SANE have two kinds of \lpar (hence of \ltens), one is linear while the other one allows free structural rules (as in polarized proof-nets). We prove confluence for SANE and give a reduction preserving encoding of $\Lambda\mu$-calculus in SANE, based on a new type system introduced by the second author. It turns out that the stream mechanism at work in $\Lambda\mu$-calculus can be explained by the associativity of the two different kinds of \lpar of SANE. At last, we achieve a Böhm theorem for SANE. This result follows Girard's program to put into the fore the separation as a key property of logic

The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results

Visible acyclic differential nets, Part I: Semantics

International audienceWe give a geometric condition that characterizes the differential nets having a finitary interpretation in finiteness spaces: visible acyclicity. This is based on visible paths, an extension to differential nets of a class of paths we introduced in the framework of linear logic nets. The characterization is then carried out as follows: the differential nets having no visible cycles are exactly those whose interpretation is a finitary relation. Visible acyclicity discloses a new kind of correctness for the promotion rule of linear logic, which goes beyond sequent calculus correctness

Confluence via strong normalisation in an algebraic \lambda-calculus with rewriting

The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic lambda-calculi are not confluent unless further restrictions are added. We provide a type system for the linear-algebraic lambda-calculus enforcing strong normalisation, which gives back confluence. The type system allows an abstract interpretation in System F.Comment: In Proceedings LSFA 2011, arXiv:1203.542

As possibilidades e o fazer da equipe do Núcleo de Apoio a Saúde da Família

Módulo 3 da Capacitação de Profissionais dos Núcleos de Apoio à Saúde da Família (NASF) do Mato Grosso do Sul. Ao iniciar a discussão sobre o Núcleo de Apoio à Saúde da Família (NASF) é importante refletir sobre o contexto em que esta equipe se insere, ou seja, compreender de maneira ampliada o Sistema Único de Saúde (SUS) assim como sua configuração em um sistema organizado em Redes de Atenção à Saúde (RAS), tendo a Atenção Básica (AB) como ordenadora do cuidado deste Sistema. A AB apresenta um alto grau de complexidade, por se caracterizar em um conjunto de ações de saúde - no âmbito individual e coletivo, que abrange a promoção e a proteção da saúde, a prevenção de agravos, o diagnóstico, o tratamento e a reabilitação. A AB tem como foco, ainda, a redução de danos e a manutenção da saúde, com o objetivo de desenvolver uma atenção integral que impacte na situação de saúde e autonomia das pessoas e nos determinantes e condicionantes de saúde das coletividades (Brasil, portaria PNAB 2011). Essas ações são desenvolvidas por meio do exercício de práticas de cuidado e gestão democráticas e participativas, sob forma de trabalho em equipe, dirigidas a populações em territórios definidos – pelas quais assume-se a responsabilidade sanitária, considerando a dinamicidade existente no lugar onde vivem essas populações