Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems

Expressiveness of Temporal Query Languages: On the Modelling of Intervals, Interval Relationships and States

Storing and retrieving time-related information are important, or even critical, tasks on many areas of Computer Science (CS) and in particular for Artificial Intelligence (AI). The expressive power of temporal databases/query languages has been studied from different perspectives, but the kind of temporal information they are able to store and retrieve is not always conveniently addressed. Here we assess a number of temporal query languages with respect to the modelling of time intervals, interval relationships and states, which can be thought of as the building blocks to represent and reason about a large and important class of historic information. To survey the facilities and issues which are particular to certain temporal query languages not only gives an idea about how useful they can be in particular contexts, but also gives an interesting insight in how these issues are, in many cases, ultimately inherent to the database paradigm. While in the area of AI declarative languages are usually the preferred choice, other areas of CS heavily rely on the extended relational paradigm. This paper, then, will be concerned with the representation of historic information in two well known temporal query languages: it Templog in the context of temporal deductive databases, and it TSQL2 in the context of temporal relational databases. We hope the results highlighted here will increase cross-fertilisation between different communities. This article can be related to recent publications drawing the attention towards the different approaches followed by the Databases and AI communities when using time-related concepts

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

Security Theorems via Model Theory

A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi). Models (interpretations) for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. Realized skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1) If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2) A protocol enforces for all xs . (phi implies for some ys . psi) iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007) to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds

Structuring an event ontology for disease outbreak detection

<p>Abstract</p> <p>Background</p> <p>This paper describes the design of an event ontology being developed for application in the machine understanding of infectious disease-related events reported in natural language text. This event ontology is designed to support timely detection of disease outbreaks and rapid judgment of their alerting status by 1) bridging a gap between layman's language used in disease outbreak reports and public health experts' deep knowledge, and 2) making multi-lingual information available.</p> <p>Construction and content</p> <p>This event ontology integrates a model of experts' knowledge for disease surveillance, and at the same time sets of linguistic expressions which denote disease-related events, and formal definitions of events. In this ontology, rather general event classes, which are suitable for application to language-oriented tasks such as recognition of event expressions, are placed on the upper-level, and more specific events of the experts' interest are in the lower level. Each class is related to other classes which represent participants of events, and linked with multi-lingual synonym sets and axioms.</p> <p>Conclusions</p> <p>We consider that the design of the event ontology and the methodology introduced in this paper are applicable to other domains which require integration of natural language information and machine support for experts to assess them. The first version of the ontology, with about 40 concepts, will be available in March 2008.</p

Towards a canonical classical natural deduction system

This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT