Modal Kleene Algebra and Partial Correctness

Modal Kleene algebras are relatives of dynamic logics that support program construction and verification by equational reasoning. We describe their application in implementing versatile program correctness components in interactive theorem provers such as Isabelle/HOL. Starting from a weakest precondition based component with a simple relational store model, we show how variants for Hoare logic, strongest postconditions and program refinement can be built in a principled way. Modularity of the approach is demonstrated by variants that capture program termination and recursion, memory models for programs with pointers, and program trace semantics.Engineering and Physical Sciences Research Council (Grant ID: REMS: Rigorous Engineering for Mainstream Systems, EP/K008528/1)This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer

Designing the ideal model for assessment of wound contamination after gunshot injuries: a comparative experimental study

<p>Abstract</p> <p>Background</p> <p>Modern high-velocity projectiles produce temporary cavities and can thus cause extensive tissue destruction along the bullet path. It is still unclear whether gelatin blocks, which are used as a well-accepted tissue simulant, allow the effects of projectiles to be adequately investigated and how these effects are influenced by caliber size.</p> <p>Method</p> <p>Barium titanate particles were distributed throughout a test chamber for an assessment of wound contamination. We fired .22-caliber Magnum bullets first into gelatin blocks and then into porcine hind limbs placed behind the chamber. Two other types of bullets (.222-caliber bullets and 6.5 × 57 mm cartridges) were then shot into porcine hind limbs. Permanent and temporary wound cavities as well as the spatial distribution of barium titanate particles in relation to the bullet path were evaluated radiologically.</p> <p>Results</p> <p>A comparison of the gelatin blocks and hind limbs showed significant differences (<it>p </it>< 0.05) in the mean results for all parameters. There were significant differences between the bullets of different calibers in the depth to which barium titanate particles penetrated the porcine hind limbs. Almost no particles, however, were found at a penetration depth of 10 cm or more. By contrast, gas cavities were detected along the entire bullet path.</p> <p>Conclusion</p> <p>Gelatin is only of limited value for evaluating the path of high-velocity projectiles and the contamination of wounds by exogenous particles. There is a direct relationship between the presence of gas cavities in the tissue along the bullet path and caliber size. These cavities, however, are only mildly contaminated by exogenous particles.</p

Exploring an interface model for CKA

Concurrent Kleene Algebras (CKAs) serve to describe general concurrent systems in a unified way at an abstract algebraic level. Recently, a graph-based model for CKA has been defined in which the incoming and outgoing edges of a graph define its input/output interface. The present paper provides a simplification and a significant extension of the original model to cover notions of states, predicates and assertions in the vein of algebraic treatments using modal semirings. Moreover, it uses the extension to set up a variant of the temporal logic CTL* for the interface model

Quantales and temporal logics

We propose an algebraic semantics for the temporal logic CTL∗ and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales. These are complete lattices with a multiplication that preserves arbitrary joins in its left argument and is isotone in its right argument. Over these quantales, the semantics of CTL∗ formulas can be encoded via finite and infinite iteration operators; the CTL and LTL operators can be related to domain operators. This yields interesting new connections between representations as known from the modal µ-calculus and Kleene/ω-algebra

On some Galois connection based abstractions for the mu-calculus

In this paper we give some abstractions that preserve sublanguages of the universal part of the branching-time µ-calculus Lµ. We first extend some results by Loiseaux et al. by using a different abstraction for the universal fragments of Lµ which are treated in their work. We show that this leads to a more elegant theoretical treatment and more practical verification methodology. After that, we define an abstraction for a universal fragment of Lµ in which the formulas can contain the -operator only under an even number of negations. The abstraction we propose is inspired by the work of Loiseaux et al., and Kesten and Pnueli. From the former we use the approach based on Galois connections, while from the latter we borrow the idea of rewriting the original formula using contracting/expanding abstractions. We argue that, besides removing some unnecessary syntactic restrictions, our approach leads to more compact and practical solutions to the abstraction problems. Keywords: abstraction, property preservation, mu-calculus, model checking

Integrating Temporal Logics

In this paper, we study the predicative semantics of different temporal logics and the relationships between them. We use a notation called generic composition to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The relationships between different temporal logics are also characterised as such modalities. Formal reasoning is carried out at the level of predicative semantics and supported by the higher-level laws of generic composition and its inverse. Various temporal domains are unified under a notion called resource cumulation. Temporal logics based on these temporal domains can be readily defined, and their axioms identified. The formalism provides a framework in which human experience about system development can be formalised as refinement laws. The approach is demonstrated in the transformation from Duration Calculus to Temporal Logic of Actions. A number of common design patterns are studied. The refinement laws identified are then applied to the case study of water pump controlling