Classical BI: Its Semantics and Proof Theory

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O'Hearn and Pym's logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave classically rather than intuitionistically (including in particular a multiplicative version of classical negation). At the semantic level, CBI-formulas have the normal bunched logic reading as declarative statements about resources, but its resource models necessarily feature more structure than those for other bunched logics; principally, they satisfy the requirement that every resource has a unique dual. At the proof-theoretic level, a very natural formalism for CBI is provided by a display calculus \`a la Belnap, which can be seen as a generalisation of the bunched sequent calculus for BI. In this paper we formulate the aforementioned model theory and proof theory for CBI, and prove some fundamental results about the logic, most notably completeness of the proof theory with respect to the semantics.Comment: 42 pages, 8 figure

Stone-Type Dualities for Separation Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

Qub: A Resource Aware Functional Programming Language

Managing resources---file handles, database connections, etc.---is a hard problem. Debugging resource leaks and runtime errors due to resource mismanagement are difficult in evolving production code. Programming languages with static type systems are great tools to ensure erroneous code is detected at compile time. However, modern static type systems do little in the aspect of resource management as resources are treated as normal values. We propose a type system, Qub, based on the logic of bunched implications (BI) which models resources as first class citizens. We distinguish two kinds of program objects---restricted and unrestricted---and two kinds of functions---sharing and separating. Our approach guarantees resource correctness without compromising existing functional abstractions

A bunch of sessions:a propositions-as-sessions interpretation of bunched implications in channel-based concurrency

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources

Morphological features of doxorubicin-resistant Walker 256 carcinosarcoma and response of mast cells

Background: The mechanisms of drug resistance of cancer have not been yet elucidated in details. Recently, the role of mast cells (MCs) in the development of drug resistance has been brought in the limelight. The aim of the study was to examine the morphological features of doxorubicin (DOX)-resistant Walker 256 carcinosarcoma and to assess the response of MCs and histamine content in these cells in relation to the development of resistance to DOX as well as in DOX-resistant tumors. Materials and Methods: The DOX resistance was induced by serial passages of Walker 256 carcinosarcoma in rats in the setting of DOX treatment in vivo. MCs in tumors were detected in the sections by staining with Toluidine Blue O. Histamine content in MCs stained with solution of Water Blue-Orcein was assessed by Astaldi semiquantitative method taking into account different staining intensity. Results: Formation of DOX resistance in the course of serial passages of Walker 256 carcinosarcoma was accompanied by the increase in the number of MCs in tumors and histamine content. Nevertheless, in tumors with phenotype of complete DOX resistance the number of histamine-containing MCs decreased to the same level as in tumors of the original strain that are DOX-sensitive. Conclusion: MCs are involved in formation of DOX resistance in Walker 256 carcinosarcoma

A Stone-type Duality Theorem for Separation Logic Via its Underlying Bunched Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because — in addition to elegant abstraction — they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality theorems for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar Boolean BI, and concluding with Separation Logic. Our results encompass all the known existing algebraic approaches to Separation Logic and prove them sound with respect to the standard store-heap semantics. We additionally recover soundness and completeness theorems of the specific truth-functional models of these logics as presented in the literature. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualises the ‘resource semantics’ interpretation underpinning Separation Logic amongst them. As a consequence, theory from those fields — as well as algebraic and topological methods — can be applied to both Separation Logic and the systems of bunched logics it is built upon. Conversely, the notion of indexed resource frame (generalizing the standard model of Separation Logic) and its associated completeness proof can easily be adapted to other non-classical predicate logics

Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Length polymorphism and head shape association among genes with polyglutamine repeats in the stalk-eyed fly, Teleopsis dalmanni

<p>Abstract</p> <p>Background</p> <p>Polymorphisms of single amino acid repeats (SARPs) are a potential source of genetic variation for rapidly evolving morphological traits. Here, we characterize variation in and test for an association between SARPs and head shape, a trait under strong sexual selection, in the stalk-eyed fly, <it>Teleopsis dalmanni</it>. Using an annotated expressed sequence tag database developed from eye-antennal imaginal disc tissues in <it>T. dalmanni </it>we identified 98 genes containing nine or more consecutive copies of a single amino acid. We then quantify variation in length and allelic diversity for 32 codon and 15 noncodon repeat regions in a large outbred population. We also assessed the frequency with which amino acid repeats are either gained or lost by identifying sequence similarities between <it>T. dalmanni </it>SARP loci and their orthologs in <it>Drosophila melanogaster</it>. Finally, to identify SARP containing genes that may influence head development we conducted a two-generation association study after assortatively mating for extreme relative eyespan.</p> <p>Results</p> <p>We found that glutamine repeats occur more often than expected by amino acid abundance among 3,400 head development genes in <it>T. dalmanni </it>and <it>D. melanogaster</it>. Furthermore, glutamine repeats occur disproportionately in transcription factors. Loci with glutamine repeats exhibit heterozygosities and allelic diversities that do not differ from noncoding dinucleotide microsatellites, including greater variation among X-linked than autosomal regions. In the majority of cases, repeat tracts did not overlap between <it>T. dalmanni </it>and <it>D. melanogaster </it>indicating that large glutamine repeats are gained or lost frequently during Dipteran evolution. Analysis of covariance reveals a significant effect of parental genotype on mean progeny eyespan, with body length as a covariate, at six SARP loci [CG33692, <it>ptip</it>, <it>band4.1 inhibitor LRP interactor</it>, <it>corto</it>, 3531953:1, and <it>ecdysone-induced protein 75B </it>(<it>Eip75B</it>)]. Mixed model analysis of covariance using the eyespan of siblings segregating for repeat length variation confirms that significant genotype-phenotype associations exist for at least one sex at five of these loci and for one gene, CG33692, longer repeats were associated with longer relative eyespan in both sexes.</p> <p>Conclusion</p> <p>Among genes expressed during head development in stalk-eyed flies, long codon repeats typically contain glutamine, occur in transcription factors and exhibit high levels of heterozygosity. Furthermore, the presence of significant associations within families between repeat length and head shape indicates that six genes, or genes linked to them, contribute genetic variation to the development of this extremely sexually dimorphic trait.</p