Completeness for a First-order Abstract Separation Logic

Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which completeness is not possible. An important element in concrete SL is the points-to predicate which denotes a singleton heap. SL with the points-to predicate has been shown to be non-recursively enumerable. In this paper, we develop a first-order SL, called FOASL, with an abstracted version of the points-to predicate. We prove that FOASL is sound and complete with respect to an abstract semantics, of which the standard SL semantics is an instance. We also show that some reasoning principles involving the points-to predicate can be approximated as FOASL theories, thus allowing our logic to be used for reasoning about concrete program verification problems. We give some example theories that are sound with respect to different variants of separation logics from the literature, including those that are incompatible with Reynolds's semantics. In the experiment we demonstrate our FOASL based theorem prover which is able to handle a large fragment of separation logic with heap semantics as well as non-standard semantics.Comment: This is an extended version of the APLAS 2016 paper with the same titl

Soundness and completeness proofs by coinductive methods

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion

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

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

Neurology

Contains reports on nineteen research projects.United States Public Health Service (B-3055-3, B-3090-3, 38101-22)United States Navy, Office of Naval Research (Contract Nonr-1841(70))Unites States Air Force (AF33(616)-7588, AFAOSR 155-63)United States Army Chemical Corps (DA-18-108-405-Cml-942)National Institutes of Health (Grant MH-04734-03)National Aeronautics and Space Administration (Grant NsG-496

General-elimination stability

General-elimination harmony articulates Gentzen's idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies' test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett's notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable.Publisher PDFPeer reviewe

An Abundant Evolutionarily Conserved CSB-PiggyBac Fusion Protein Expressed in Cockayne Syndrome

Cockayne syndrome (CS) is a devastating progeria most often caused by mutations in the CSB gene encoding a SWI/SNF family chromatin remodeling protein. Although all CSB mutations that cause CS are recessive, the complete absence of CSB protein does not cause CS. In addition, most CSB mutations are located beyond exon 5 and are thought to generate only C-terminally truncated protein fragments. We now show that a domesticated PiggyBac-like transposon PGBD3, residing within intron 5 of the CSB gene, functions as an alternative 3′ terminal exon. The alternatively spliced mRNA encodes a novel chimeric protein in which CSB exons 1–5 are joined in frame to the PiggyBac transposase. The resulting CSB-transposase fusion protein is as abundant as CSB protein itself in a variety of human cell lines, and continues to be expressed by primary CS cells in which functional CSB is lost due to mutations beyond exon 5. The CSB-transposase fusion protein has been highly conserved for at least 43 Myr since the divergence of humans and marmoset, and appears to be subject to selective pressure. The human genome contains over 600 nonautonomous PGBD3-related MER85 elements that were dispersed when the PGBD3 transposase was last active at least 37 Mya. Many of these MER85 elements are associated with genes which are involved in neuronal development, and are known to be regulated by CSB. We speculate that the CSB-transposase fusion protein has been conserved for host antitransposon defense, or to modulate gene regulation by MER85 elements, but may cause CS in the absence of functional CSB protein

Rpb1 Sumoylation in Response to UV Radiation or Transcriptional Impairment in Yeast

Covalent modifications of proteins by ubiquitin and the Small Ubiquitin-like MOdifier (SUMO) have been revealed to be involved in a plethora of cellular processes, including transcription, DNA repair and DNA damage responses. It has been well known that in response to DNA damage that blocks transcription elongation, Rpb1, the largest subunit of RNA polymerase II (Pol II), is ubiquitylated and subsequently degraded in mammalian and yeast cells. However, it is still an enigma regarding how Pol II responds to damaged DNA and conveys signal(s) for DNA damage-related cellular processes. We found that Rpb1 is also sumoylated in yeast cells upon UV radiation or impairment of transcription elongation, and this modification is independent of DNA damage checkpoint activation. Ubc9, an E2 SUMO conjugase, and Siz1, an E3 SUMO ligase, play important roles in Rpb1 sumoylation. K1487, which is located in the acidic linker region between the C-terminal domain and the globular domain of Rpb1, is the major sumoylation site. Rpb1 sumoylation is not affected by its ubiquitylation, and vice versa, indicating that the two processes do not crosstalk. Abolishment of Rpb1 sumoylation at K1487 does not affect transcription elongation or transcription coupled repair (TCR) of UV-induced DNA damage. However, deficiency in TCR enhances UV-induced Rpb1 sumoylation, presumably due to the persistence of transcription-blocking DNA lesions in the transcribed strand of a gene. Remarkably, abolishment of Rpb1 sumoylation at K1487 causes enhanced and prolonged UV-induced phosphorylation of Rad53, especially in TCR-deficient cells, suggesting that the sumoylation plays a role in restraining the DNA damage checkpoint response caused by transcription-blocking lesions. Our results demonstrate a novel covalent modification of Rpb1 in response to UV induced DNA damage or transcriptional impairment, and unravel an important link between the modification and the DNA damage checkpoint response

Automated Detection of External Ventricular and Lumbar Drain-Related Meningitis Using Laboratory and Microbiology Results and Medication Data

OBJECTIVE: Monitoring of healthcare-associated infection rates is important for infection control and hospital benchmarking. However, manual surveillance is time-consuming and susceptible to error. The aim was, therefore, to develop a prediction model to retrospectively detect drain-related meningitis (DRM), a frequently occurring nosocomial infection, using routinely collected data from a clinical data warehouse. METHODS: As part of the hospital infection control program, all patients receiving an external ventricular (EVD) or lumbar drain (ELD) (2004 to 2009; n = 742) had been evaluated for the development of DRM through chart review and standardized diagnostic criteria by infection control staff; this was the reference standard. Children, patients dying <24 hours after drain insertion or with <1 day follow-up and patients with infection at the time of insertion or multiple simultaneous drains were excluded. Logistic regression was used to develop a model predicting the occurrence of DRM. Missing data were imputed using multiple imputation. Bootstrapping was applied to increase generalizability. RESULTS: 537 patients remained after application of exclusion criteria, of which 82 developed DRM (13.5/1000 days at risk). The automated model to detect DRM included the number of drains placed, drain type, blood leukocyte count, C-reactive protein, cerebrospinal fluid leukocyte count and culture result, number of antibiotics started during admission, and empiric antibiotic therapy. Discriminatory power of this model was excellent (area under the ROC curve 0.97). The model achieved 98.8% sensitivity (95% CI 88.0% to 99.9%) and specificity of 87.9% (84.6% to 90.8%). Positive and negative predictive values were 56.9% (50.8% to 67.9%) and 99.9% (98.6% to 99.9%), respectively. Predicted yearly infection rates concurred with observed infection rates. CONCLUSION: A prediction model based on multi-source data stored in a clinical data warehouse could accurately quantify rates of DRM. Automated detection using this statistical approach is feasible and could be applied to other nosocomial infections