An Intuitionistic Formula Hierarchy Based on High-School Identities

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e. sequent) isomorphisms corresponding to the high-school identities, we show that one can obtain a more compact variant of a proof system, consisting of non-invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalisation procedure. Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non-invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first-order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism

A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

On the computational content of Zorn's lemma

We give a computational interpretation to an abstract instance of Zorn's lemma formulated as a wellfoundedness principle in the language of arithmetic in all finite types. This is achieved through G\"odel's functional interpretation, and requires the introduction of a novel form of recursion over non-wellfounded partial orders whose existence in the model of total continuous functionals is proven using domain theoretic techniques. We show that a realizer for the functional interpretation of open induction over the lexicographic ordering on sequences follows as a simple application of our main results

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems

Neurology

Contains reports on seven research projects.U. S. Public Health Service (B-3055-3,U. S. Public Health Service (B-3090-3)U. S. Public Health Service (38101-22)Office of Naval Research (Nonr-1841 (70))Air Force (AF33(616)-7588)Air Force (AFAOSR 155-63)Army Chemical Corps (DA-18-108-405-Cml-942)National Institutes of Health (Grant MH-04734-03

Successful control of a hospital-wide outbreak of OXA-48 producing Enterobacteriaceae in the Netherlands, 2009 to 2011

On 31 May 2011, after notification of Klebsiella pneumoniae(KP)(OXA-48);(CTX-M-15) in two patients, nosocomial transmission was suspected in a Dutch hospital. Hospital-wide infection control measures and an outbreak investigation were initiated. A total of 72,147 patients were categorised into groups based on risk of OXA-48 colonisation or infection, and 7,527 were screened for Enterobacteriaceae(OXA-48) by polymerase chain reaction (PCR). Stored KP isolates (n=408) were retrospectively tested for OXA-48 and CTX-M-1 group extended-spectrum beta-lactamases (ESBL). 285 KP isolates from retrospective and prospective patient screening were genotyped by amplified fragment length polymorphism (AFLP). 41 isolates harbouring different Enterobacteriaceae species were analysed by plasmid multilocus sequence typing (pMLST). No nosocomial transmission of Enterobacteriaceae(OXA-48) was detected after 18 July 2011. Enterobacteriaceae(OXA-48) were found in 118 patients (KP (n=99), Escherichia coli (n=56), >= 1 Enterobacteriaceae(OXA-48) species (n=52)),of whom 21 had clinical infections. 39/41 (95%) of OXA-48 containing plasmids were identical in pMLST. Minimum inhibitory concentrations (MICs) of KPOXA-48 and E. coli(OXA-48) for imipenem and meropenem ranged from = 16 mg/L, and 153/157 (97%) had MIC >0.25mg/L for ertapenem. AFLP identified a cluster of 203 genetically linked isolates (62 KPOXA-48;(CTX-M15); 107 KPCTX-M-15; 34 KPOXA-48). The 'oldest' KPCTX-M-15 and KPOXA-48 clonal types originated from February 2009 and September 2010, respectively. The last presumed outbreak-related KPOXA-48 was detected in April 2012. Uncontrolled transmission of KP (CTX-M-15) evolved into a nosocomial outbreak of KPOXA-48; CTX-M15 with large phenotypical heterogeneity. Although the outbreak was successfully controlled, the contribution of individual containment measures and of the hospital relocating into a new building just before outbreak notification was impossible to quantify

Radical addition polymerization of acrylates in a Buss-Kneader

The radical addn. co-polymn. of 2-hydroxyethyl methacrylate and Bu acrylate is carried out in a continuously operating Buss-Kneader. To calc. temp. profiles over the length of the kneader the heat balance is solved. For the heat transfer coeff. a model based on the penetration theory is used. This model is exptl. verified. The reaction kinetics of the radical addn. polymn. are studied in a differential scanning calorimeter. The polymn. kinetics are modeled using non-stationary radical concns. The calcd. temp. profiles over the length of the Buss-Kneader are a good approxn. of the exptl. data. [on SciFinder (R)