Infinets: The parallel syntax for non-wellfounded proof-theory

Logics based on the µ-calculus are used to model induc-tive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization. Inductive and coinductive reasoning is pervasive in computer science to specify and reason about infinite data as well as reactive properties. Developing appropriate proof systems amenable to automated reasoning over (co)inductive statements is therefore important for designing programs as well as for analyzing computational systems. Various logical settings have been introduced to reason about such inductive and coinductive statements, both at the level of the logical languages modelling (co)induction (such as Martin Löf's inductive predicates or fixed-point logics, also known as µ-calculi) and at the level of the proof-theoretical framework considered (finite proofs with explicit (co)induction rulesà la Park [23] or infinite, non-wellfounded proofs with fixed-point unfold-ings) [6-8, 4, 1, 2]. Moreover, such proof systems have been considered over classical logic [6, 8], intuitionistic logic [9], linear-time or branching-time temporal logic [19, 18, 25, 26, 13-15] or linear logic [24, 16, 4, 3, 14]

On the Proof Theory of Regular Fixed Points

International audienceWe consider encoding finite automata as least fixed points in a proof theoretical framework equipped with a general induction scheme, and study automata inclusion in that setting. We provide a coinductive characterization of inclusion that yields a natural bridge to proof-theory. This leads us to generalize these observations to regular formulas, obtaining new insights about inductive theorem proving and cyclic proofs in particular

Extracting Proofs from Tabled Proof Search

We consider the problem of model checking specifications involving co-inductive definitions such as are available for bisimulation. A proof search approach to model checking with such specifications often involves state exploration. We consider four different tabling strategies that can minimize such exploration significantly. In general, tabling involves storing previously proved subgoals and reusing (instead of reproving) them in proof search. In the case of co-inductive proof search, tables allow a limited form of loop checking, which is often necessary for, say, checking bisimulation of non-terminating processes. We enhance the notion of tabled proof search by allowing a limited deduction from tabled entries when performing table lookup. The main problem with this enhanced tabling method is that it is generally unsound when co-inductive definitions are involved and when tabled entries contain unproved entries. We design a proof system with tables and show that by managing tabled entries carefully, one would still be able to obtain a sound proof system. That is, we show how one can extract a post-fixed point from a tabled proof for a co-inductive goal. We then apply this idea to the technique of bisimulation ''up-to'' commonly used in process algebra

Association Between CNDP1 Genotype and Diabetic Nephropathy Is Sex Specific

OBJECTIVE-The 5-5 homozygous CNDP1 (carnosinase) genotype is associated with a reduced risk of diabetic nephropathy. We investigated whether this association is sex specific and independent of susceptibility for type 2 diabetes. RESEARCH DESIGN AND METHODS-Three separate groups of 114, 90, and 66 patients with type 2 diabetes and diabetic nephropathy were included in this study and compared with 93 patients with type 2 diabetes for >15 years without diabetic nephropathy and 472 population control subjects. The diabetes control group was used to determine an association in the three patient groups separately, and the population control group was used to estimate the genotype risk [odds ratio (CI)] for the population in a pooled analysis. The population control subjects were also compared with 562 patients with type 2 diabetes without diabetic nephropathy to determine whether the association was independent of type 2 diabetes. The CNDP1 genotype was determined by fragment analysis after PCR amplification. RESULTS-The frequency of the 5-5 homozygous genotype was 28, 36, and 41% in the three diabetic nephropathy patient groups and 43 and 42% in the diabetic and population control subjects, respectively. The 5-5 homozygous genotype occurred significantly less frequently in women in all three patient groups compared with diabetic control subjects. The genotype risk for the population was estimated to be 0.5 (0.30-0.68) in women and 1.2 (0.77-1.69) in men. The 562 patients with type 2 diabetes without diabetic nephropathy did not differ from the general population (P = 0.23). CONCLUSIONS-This study suggests that the association between the CNDP1 gene and diabetic nephropathy is sex specific and independent of susceptibility for type 2 diabetes. Diabetes 59:1555-1559, 201

Genetic associations in diabetic nephropathy: a meta-analysis

Diabetes mellitus: pathophysiological changes and therap

Observed communication semantics for classical processes

Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication, and use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences

Bi-allelic <i>NIT1 </i>variants cause a brain small vessel disease characterized by movement disorders, massively dilated perivascular spaces, and intracerebral hemorrhage

Purpose: To describe a recessively inherited cerebral small vessel disease, caused by loss-of-function variants in Nitrilase1 (NIT1). Methods:We performed exome sequencing, brain magnetic resonance imaging, neuropathology, electron microscopy, western blotting, and transcriptomic and metabolic analyses in 7 NIT1-small vessel disease patients from 5 unrelated pedigrees. Results: The first identified patients were 3 siblings, compound heterozygous for the NIT1 c.727C&gt;T; (p.Arg243Trp) variant and the NIT1 c.198_199del; p.(Ala68∗) variant. The 4 additional patients were single cases from 4 unrelated pedigrees and were all homozygous for the NIT1 c.727C&gt;T; p.(Arg243Trp) variant. Patients presented in mid-adulthood with movement disorders. All patients had striking abnormalities on brain magnetic resonance imaging, with numerous and massively dilated basal ganglia perivascular spaces. Three patients had non-lobar intracerebral hemorrhage between age 45 and 60, which was fatal in 2 cases. Western blotting on patient fibroblasts showed absence of NIT1 protein, and metabolic analysis in urine confirmed loss of NIT1 enzymatic function. Brain autopsy revealed large electron-dense deposits in the vessel walls of small and medium sized cerebral arteries. Conclusion: NIT1-small vessel disease is a novel, autosomal recessively inherited cerebral small vessel disease characterized by a triad of movement disorders, massively dilated basal ganglia perivascular spaces, and intracerebral hemorrhage.</p

Bi-allelic <i>NIT1 </i>variants cause a brain small vessel disease characterized by movement disorders, massively dilated perivascular spaces, and intracerebral hemorrhage

Purpose: To describe a recessively inherited cerebral small vessel disease, caused by loss-of-function variants in Nitrilase1 (NIT1). Methods:We performed exome sequencing, brain magnetic resonance imaging, neuropathology, electron microscopy, western blotting, and transcriptomic and metabolic analyses in 7 NIT1-small vessel disease patients from 5 unrelated pedigrees. Results: The first identified patients were 3 siblings, compound heterozygous for the NIT1 c.727C&gt;T; (p.Arg243Trp) variant and the NIT1 c.198_199del; p.(Ala68∗) variant. The 4 additional patients were single cases from 4 unrelated pedigrees and were all homozygous for the NIT1 c.727C&gt;T; p.(Arg243Trp) variant. Patients presented in mid-adulthood with movement disorders. All patients had striking abnormalities on brain magnetic resonance imaging, with numerous and massively dilated basal ganglia perivascular spaces. Three patients had non-lobar intracerebral hemorrhage between age 45 and 60, which was fatal in 2 cases. Western blotting on patient fibroblasts showed absence of NIT1 protein, and metabolic analysis in urine confirmed loss of NIT1 enzymatic function. Brain autopsy revealed large electron-dense deposits in the vessel walls of small and medium sized cerebral arteries. Conclusion: NIT1-small vessel disease is a novel, autosomal recessively inherited cerebral small vessel disease characterized by a triad of movement disorders, massively dilated basal ganglia perivascular spaces, and intracerebral hemorrhage.</p

Advances in Property-Based Testing for αProlog

$\alpha$Check is a light-weight property-based testing tool built on top of $\alpha$Prolog, a logic programming language based on nominal logic. $\alpha$Prolog is particularly suited to the validation of the meta-theory of formal systems, for example correctness of compiler translations involving name-binding, alpha-equivalence and capture-avoiding substitution. In this paper we describe an alternative to the negation elimination algorithm underlying $\alpha$Check that substantially improves its effectiveness. To substantiate this claim we compare the checker performances w.r.t. two of its main competitors in the logical framework niche, namely the QuickCheck/Nitpick combination offered by Isabelle/HOL and the random testing facility in PLT-Redex.Comment: To appear, Tests and Proofs 2016; includes appendix with details not in the conference versio