Presupposition projection as proof construction

Even though Van der Sandt's presuppositions as anaphora approach is empirically successful, it fails to give a formal account of the interaction between world-knowledge and presuppositions. In this paper, an algorithm is sketched which is based on the idea of presuppositions as anaphora. It improves on this approach by employing a deductive system, Constructive Type Theory (CTT), to get a formal handle on the way world-knowledge influences presupposition projection. In CTT, proofs for expressions are explicitly represented as objects. These objects can be seen as a generalization of DRT's discourse markers. They are useful in dealing with presuppositional phenomena which require world-knowledge, such as Clark's bridging examples and Beaver's conditional presuppositions

A coalgebraic view of bar recursion and bar induction

We reformulate the bar recursion and induction principles in terms of recursive and wellfounded coalgebras. Bar induction was originally proposed by Brouwer as an axiom to recover certain classically valid theorems in a constructive setting. It is a form of induction on non- wellfounded trees satisfying certain properties. Bar recursion, introduced later by Spector, is the corresponding function defnition principle. We give a generalization of these principles, by introducing the notion of barred coalgebra: a process with a branching behaviour given by a functor, such that all possible computations terminate. Coalgebraic bar recursion is the statement that every barred coalgebra is recursive; a recursive coalgebra is one that allows defnition of functions by a coalgebra-to-algebra morphism. It is a framework to characterize valid forms of recursion for terminating functional programs. One application of the principle is the tabulation of continuous functions: Ghani, Hancock and Pattinson defned a type of wellfounded trees that represent continuous functions on streams. Bar recursion allows us to prove that every stably continuous function can be tabulated to such a tree where by stability we mean that the modulus of continuity is also continuous. Coalgebraic bar induction states that every barred coalgebra is well-founded; a wellfounded coalgebra is one that admits proof by induction

Gender differences in health of EU10 and EU15 populations: the double burden of EU10 men

This study compares gender differences in Healthy Life Years (HLY) and unhealthy life years (ULY) between the original (EU15) and new member states (EU10). Based on the number of deaths, population and prevalence of activity limitations from the Statistics of Living and Income Conditions Survey (SILC) survey, we calculated HLY and ULY for the EU10 and EU15 in 2006 with the Sullivan method. We used decomposition analysis to assess the contributions of mortality and disability and age to gender differences in HLY and ULY. HLY at age 15 for women in the EU10 were 3.1 years more than those for men at the same age, whereas HLY did not differ by gender in the EU15. In both populations ULY at age 15 for women exceeded those for men by 5.5 years. Decomposition showed that EU10 women had more HLY because higher disability in women only partially offset (−0.8 years) the effect of lower mortality (+3.9 years). In the EU15 women’s higher disability prevalence almost completely offset women’s lower mortality. The 5.3 fewer ULY in EU10 men than in EU10 women mainly reflected higher male mortality (4.5 years), while the fewer ULY in EU15 men than in EU15 women reflected both higher male mortality (2.9 years) and higher female disability (2.6 years). The absence of a clear gender gap in HLY in the EU15 thus masked important gender differences in mortality and disability. The similar size of the gender gap in ULY in the EU-10 and EU-15 masked the more unfavourable health situation of EU10 men, in particular the much stronger and younger mortality disadvantage in combination with the virtually absent disability advantage below age 65 in men

Explicit Auditing

The Calculus of Audited Units (CAU) is a typed lambda calculus resulting from a computational interpretation of Artemov's Justification Logic under the Curry-Howard isomorphism; it extends the simply typed lambda calculus by providing audited types, inhabited by expressions carrying a trail of their past computation history. Unlike most other auditing techniques, CAU allows the inspection of trails at runtime as a first-class operation, with applications in security, debugging, and transparency of scientific computation. An efficient implementation of CAU is challenging: not only do the sizes of trails grow rapidly, but they also need to be normalized after every beta reduction. In this paper, we study how to reduce terms more efficiently in an untyped variant of CAU by means of explicit substitutions and explicit auditing operations, finally deriving a call-by-value abstract machine

A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

Labelled Graph Rewriting Meets Social Networks

International audienceThe intense development of computing techniques and the increasing volumes of produced data raise many modelling and analysis challenges. There is a need to represent and analyse information that is: complex –due to the presence of massive and highly heterogeneous data–, dynamic –due to interactions, time, external and internal evolutions–, connected and distributed in networks. We argue in this work that relevant concepts to address these challenges are provided by three ingredients: labelled graphs to represent networks of data or objects; rewrite rules to deal with concurrent local transformations; strategies to express control versus autonomy and to focus on points of interests. To illustrate the use of these concepts, we choose to focus our interest on social networks analysis, and more precisely in this paper on random network generation. Labelled graph strategic rewriting provides a formalism in which different models can be generated and compared. Conversely, the study of social networks, with their size and complexity, stimulates the search for structure and efficiency in graph rewriting. It also motivated the design of new or more general kinds of graphs, rules and strategies (for instance, to define positions in graphs), which are illustrated here. This opens the way to further theoretical and practical questions for the rewriting community

The Completeness of BCD for an Operational Semantics

We give a completeness theorem for the BCD theory of intersection types in an operational semantics based on logical relations