A Spatial Equational Logic for the Applied π-Calculus

Abstract

Abstract. Spatial logics have been proposed to reason locally and modularly on algebraic models of distributed systems. In this paper we define the spatial equational logic AπLwhose models are processes of the applied π-calculus. This extension of the π-calculus allows term manipulation and records communications as active substitutions in a frame, thus augmenting the underlying predefined equational theory. Our logic allows one to reason locally either on frames or on processes, thanks to static and dynamic spatial operators. We study the logical equivalences induced by various relevant fragments of AπL, and show in particular that the whole logic induces a coarser equivalence than structural congruence. We give characteristic formulae for some of these equivalences and for static equivalence. Going further into the exploration of AπL's expressivity, we also show that it can eliminate standard term quantification.

Theory of Security and Applications

“…In this paper, we study the decidability of the model-checking of AπL [18,17], a spatial logic for the applied π-calculus, and more precisely of a fragment FSL of it we call frame spatial logic, that is dedicated to frames. This fragment exposes two of the main ingredients of AπL, hidden name revelation and spatial conjunction, which we believe to be generally useful in naturally expressing security properties of frames.…”

Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus

“…In this paper, we study the decidability of the model-checking of AπL [20,19], a spatial logic for the applied π-calculus, and more precisely of a fragment FSL of it we call frame spatial logic, that is dedicated to frames. This fragment exposes two of the main ingredients of AπL, hidden name revelation and spatial conjunction, which we believe to be generally useful in naturally expressing security properties of frames.…”

A Spatial-Epistemic Logic for Reasoning about Security Protocols

“…In this paper we propose a framework for protocol analysis based on process calculus models and logic specifications. While the usage of process calculi and logic in this context is not new [14,8,2], our approach stems from the fact that many interesting properties of such systems are often a function of what information the several parts of a system may or may not obtain. While other frameworks (e.g., Avispa [4] and Casper [13]) allow one to efficiently verify a wide range of interesting security properties, these are not usually stated in this high-level knowledge oriented approach.…”