Bigraphical Logics for XML

Bigraphs have been recently proposed as a meta-model for global computing resources; they are built orthogonally on two structures: a hierarchical ‘place’ graph for locations and a ‘link’ (hyper-)graph for connections. XML is now the standard meta-language for the data exchange and storage on the web. In this paper we address the similarities between bigraphs and XML and we propose bigraphs as a rich model for XML (and XML contexts). Building on this idea we proceed by investigating how the recently proposed logic of BiLog can be instantiated to describe, query and reason about web data (and web contexts)

Spatial Logics for Bigraphs

Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts

Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of

Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

A logic for application level QoS

Service Oriented Computing (SOC) has been proposed as a paradigm to describe computations of applications on wide area distributed systems. Awareness of Quality of Service (QoS) is emerging as a new exigency in both design and implementation of SOC applications. We do not refer to QoS aspects related to low-level performance and focus on those high-level non-functional features perceived by end-users as application dependent requirements, e.g., the price of a given service, or the payment mode, or else the availability of a resource (e.g., a file in a given format). In this paper we present a logic which includes mechanisms to consider the three main dimensions of systems, namely their structure, behaviour and QoS aspects. The evaluation of a formula is a value of a constraint-semiring and not just a boolean value expressing whether or not the formula holds. This permits to express not only topological and temporal properties but also QoS properties of systems. The logic is interpreted on SHReQ, a formal framework for specifying systems that handles abstract high-level QoS aspects combining Synchronised Hyperedge Replacement with constraint-semirings

Elimination of spatial connectives in static spatial logics

AbstractThe recent interest for specification on resources yields so-called spatial logics, that is specification languages offering new forms of reasoning: the local reasoning through the separation of the resource space into two disjoint subspaces, and the contextual reasoning through hypothetical extension of the resource space.We consider two resource models and their related logics:•The static ambient model, proposed as an abstraction of semistructured data (Proc. ESOP’01, Lecture Notes in Computer Science, vol. 2028, Springer, Berlin, 2001, pp. 1–22 (invited paper)) with the static ambient logic (SAL) that was proposed as a request language, both obtained by restricting the mobile ambient calculus (Proc. FOSSACS’98, Lecture Notes in Computer Science, vol. 1378, Springer, Berlin, 1998, pp. 140–155) and logic (Proc. POPL’00, ACM Press, New York, 2000, pp. 365–377) to their purely static aspects.•The memory model and the assertion language of separation logic, both defined in Reynolds (Proc. LICS’02, 2002) for the purpose of the axiomatic semantic of imperative programs manipulating pointers.We raise the questions of the expressiveness and the minimality of these logics. Our main contribution is a minimalisation technique we may apply for these two logics. We moreover show some restrictions of this technique for the extension SAL∀ with universal quantification, and we establish the minimality of the adjunct-free fragment (SALint)

An observational model for spatial logics

Spatiality is an important aspect of distributed systems because their computations depend both on the dynamic behaviour and on the structure of their components. Spatial logics have been proposed as the formal device for expressing spatial properties of systems. We define CCS∥, a CCS-like calculus whose semantics allows one to observe spatial aspects of systems on the top of which we define models of the spatial logic. Our alternative definition of models is proved equivalent to the standard one. Furthermore, logical equivalence is characterized in terms of the bisimilarity of CCS∥

Names and Binding in Type Theory

Names and name-binding are useful concepts in the theory and practice of formal systems. In this thesis we study them in the context of dependent type theory. We propose a novel dependent type theory with primitives for the explicit handling of names. As the main application, we consider programming and reasoning with abstract syntax involving variable binders. Gabbay and Pitts have shown that Fraenkel Mostowski (FM) set theory models a notion of name using which informal work with names and binding can be made precise. They have given a number of useful constructions for working with names and binding, such as a syntax-independent notion of freshness that formalises when two objects do not share names, and a freshness quantifier that simplifies working with names and binding. Related to FM set theory, a number of systems for working with names have been given, among them are the first-order Nominal Logic, the higher-order logic FM-HOL, the Theory of Contexts as well as the programming language FreshML. In this thesis we study how dependent type theory can be extended with primitives for working with names and binding. Our choice of primitives is different from that in FM set theory. In FM set theory the fundamental primitive for working with names is swapping. All other concepts such as \alpha-equivalence classes and binding are constructed from it. For dependent type theory, however, this approach of constructing everything from swapping is not ideal, since it requires us to make strong assumptions on the type theory. For instance, the construction of \alpha-equivalence classes from swapping appears to require quotient types. Our approach is to treat constructions such as \alpha-equivalence classes and name-binding directly, turning them into primitives of the type theory. To do this, it is convenient to take freshness rather than swapping as the fundamental primitive. Based on the close correspondence between type theories and categories, we approach the design of the dependent type theory by studying the categorical structure underlying FM set theory. We start from a monoidal structure capturing freshness. By analogy with the definition of simple dependent sums \Sigma and products \Pi from the cartesian product, we define monoidal dependent sums \Sigma^* and products \Pi^* from the monoidal structure. For the type of names N, we have an isomorphism \Sigma^*_N\iso\Pi^*_N generalising the freshness quantifier. We show that this structure includes \alpha-equivalence classes, name binding, unique choice of fresh names as well as the freshness quantifier. In addition to the set theoretic model corresponding to FM set theory, we also give a realizability model of this structure. The semantic structure leads us to a bunched type theory having both a dependent additive context structure and a non-dependent multiplicative context structure. This type theory generalises the simply-typed \alpha\lambda-calculus of O'Hearn and Pym in the additive direction. It includes novel monoidal products \Pi^* and sums \Sigma^* as well as hidden-name types H for working with names and binding. We give examples for the use of the type theory for programming and reasoning with abstract syntax involving binders. We show that abstract syntax can be handled both in the style of FM set theory and in the style of Weak Higher Order Abstract Syntax. Moreover, these two styles of working with abstract syntax can be mixed, which has interesting applications such as the derivation of a term for the unique choice of new names