A proof-theoretic analysis of the classical propositional matrix method

The matrix method, due to Bibel and Andrews, is a proof procedure designed for automated theorem-proving. We show that underlying this method is a fully structured combinatorial model of conventional classical proof theory. © 2012 The Author, 2012. Published by Oxford University Press

Intuitionistic layered graph logic

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give soundness and completeness theorems for labelled tableaux and Hilbert-type systems with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent a range of systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied

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

Discrete Choice, Social Interaction, and Policy in Encryption Technology Adoption

We introduce a model for examining the factors that lead to the adoption of new encryption technologies. Building on the work of Brock and Durlauf, the model describes how agents make choices, in the presence of social interaction, between competing technologies given their relative cost, functionality, and usability. We apply the model to examples about the adoption of encryption in communication (email and messaging) and storage technologies (self-encrypting drives) and also consider our model’s predictions for the evolution of technology adoption over time

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

Practicing a Science of Security: A Philosophy of Science Perspective

Our goal is to refocus the question about cybersecurity research from 'is this process scientific' to 'why is this scientific process producing unsatisfactory results'. We focus on five common complaints that claim cybersecurity is not or cannot be scientific. Many of these complaints presume views associated with the philosophical school known as Logical Empiricism that more recent scholarship has largely modified or rejected. Modern philosophy of science, supported by mathematical modeling methods, provides constructive resources to mitigate all purported challenges to a science of security. Therefore, we argue the community currently practices a science of cybersecurity. A philosophy of science perspective suggests the following form of practice: structured observation to seek intelligible explanations of phenomena, evaluating explanations in many ways, with specialized fields (including engineering and forensics) constraining explanations within their own expertise, inter-translating where necessary. A natural question to pursue in future work is how collecting, evaluating, and analyzing evidence for such explanations is different in security than other sciences

A System of Interaction and Structure II: The Need for Deep Inference

This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports deep inference, in which inference rules can be applied anywhere inside logical expressions. The use of deep inference results in a simple logical system for MLL extended with the self-dual non-commutative operator, which has been to date not known to be expressible in sequent calculus. In this paper, deep inference is shown to be crucial for the logic BV, that is, any restriction on the ``depth'' of the inference rules of BV would result in a strictly less expressive logical system

Trust economics feasibility study

We believe that enterprises and other organisations currently lack sophisticated methods and tools to determine if and how IT changes should be introduced in an organisation, such that objective, measurable goals are met. This is especially true when dealing with security-related IT decisions. We report on a feasibility study, Trust Economics, conducted to demonstrate that such methodology can be developed. Assuming a deep understanding of the IT involved, the main components of our trust economics approach are: (i) assess the economic or financial impact of IT security solutions; (ii) determine how humans interact with or respond to IT security solutions; (iii) based on above, use probabilistic and stochastic modelling tools to analyse the consequences of IT security decisions. In the feasibility study we apply the trust economics methodology to address how enterprises should protect themselves against accidental or malicious misuse of USB memory sticks, an acute problem in many industries

Portfolio-based appraisal: superficial or useful?

This paper outlines the growing role played by performance appraisal within medical regulation, supported by learning portfolios. It investigates if these are superficial or useful tools. In doing so it argues that caution must be exercised in promoting such tools to help modernise medical regulatory frameworks

The homeobox transcription factor Even-skipped regulates acquisition of electrical properties in Drosophila neurons.

BACKGROUND: While developmental processes such as axon pathfinding and synapse formation have been characterized in detail, comparatively less is known of the intrinsic developmental mechanisms that regulate transcription of ion channel genes in embryonic neurons. Early decisions, including motoneuron axon targeting, are orchestrated by a cohort of transcription factors that act together in a combinatorial manner. These transcription factors include Even-skipped (Eve), islet and Lim3. The perdurance of these factors in late embryonic neurons is, however, indicative that they might also regulate additional aspects of neuron development, including the acquisition of electrical properties. RESULTS: To test the hypothesis that a combinatorial code transcription factor is also able to influence the acquisition of electrical properties in embryonic neurons we utilized the molecular genetics of Drosophila to manipulate the expression of Eve in identified motoneurons. We show that increasing expression of this transcription factor, in two Eve-positive motoneurons (aCC and RP2), is indeed sufficient to affect the electrical properties of these neurons in early first instar larvae. Specifically, we observed a decrease in both the fast K+ conductance (IKfast) and amplitude of quantal cholinergic synaptic input. We used charybdotoxin to pharmacologically separate the individual components of IKfast to show that increased Eve specifically down regulates the Slowpoke (a BK Ca2+-gated potassium channel), but not Shal, component of this current. Identification of target genes for Eve, using DNA adenine methyltransferase identification, revealed strong binding sites in slowpoke and nAcRalpha-96Aa (a nicotinic acetylcholine receptor subunit). Verification using real-time PCR shows that pan-neuronal expression of eve is sufficient to repress transcripts for both slo and nAcRalpha-96Aa. CONCLUSION: Taken together, our findings demonstrate, for the first time, that Eve is sufficient to regulate both voltage- and ligand-gated currents in motoneurons, extending its known repertoire of action beyond its already characterized role in axon guidance. Our data are also consistent with a common developmental program that utilizes a defined set of transcription factors to determine both morphological and functional neuronal properties