Laboratory We introduce a calculus describing the movement of processes and devices, including movement through administrative domains.

We consider a propositional spatial logic for finite trees. The logic includes (tree composition), (the implication induced by composition), and 0 (the unit of composition) . We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logic-based type systems for semistructured data. We describe a small programming language based on this idea.

this paper we present TQL, a query language for semistructured data that is based on the ambient logic

We prove the decidability of the quantifier-free, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic and counting constraints on (nested) vectors of integers.

In addition to behavioral properties, spatial logics can talk about other key properties of concurrent systems such as secrecy, freshness, usage of resources, and distribution. We study an expressive spatial logic for systems specified in the synchronous pi-calculus with recursion, based on a small set of behavioral and spatial observations. We give coinductive and equational characterizations of the equivalence induced on processes by the logic, and conclude that it strictly lies between structural congruence and strong bisimulation. We then show that model-checking is decidable for a useful class of processes that includes the finite-control fragment of the pi-calculus.

We introduce a rich language of descriptions for semistructured tree-like data, and we explain how such descriptions relate to the data they describe. Various query languages and data schemas can be based on such descriptions. 1

We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the logic with and without recursion, and with either an exponential or a linear version of the basic composition operator. We study the combined complexity and the expressive power of the four combinations. We prove that, without recursion, the linear and exponential versions of the logic correspond to significant fragments of first-order (FO) and monadic second-order (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched with-style recursion, their expressive power is sharply increased. Both are able to express PSPACE-complete problems, although their combined complexity and data complexity still belong to PSPACE.

In this paper we investigate the quantifier-free fragment of the TQL logic proposed by Cardelli and Ghelli. The TQL logic, inspired from the ambient logic, is the core of a query language for semistructured data represented as unranked and unordered trees. The fragment we consider here, named STL, contains as main features spatial composition and location as well as a fixed point construct. We prove that satisfiability for STL is undecidable. We show also that STL is strictly more expressive than the Presburger monadic second-order logic (PMSO) of Seidl, Schwentick and Muscholl when interpreted over unranked and unordered edge-labelled trees. We define a class of tree automata whose transitions are conditioned by arithmetical constraints; we show then how to compute from a closed STL formula a tree automaton accepting precisely the models of the formula. Finally, still using our tree automata framework, we exhibit some syntactic restrictions over STL formulae that allow us to capture precisely the logics MSO and PMSO. 1

The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the non-standard fresh quantifier (I). This work adresses the questions of expressiveness and minimality of SAL from the point of view of adjuncts. We define the intensional fragment of the logic (SALint), the logic without adjuncts, and prove that it captures all the expressiveness of the logic. We moreover study the question of adjuncts elimination in SAL ∀ , where I quantifier is replaced by the classical ∀ quantifier. We conclude with a proof of the minimality of SALint.

We study decidability of a logic for describing processes with restricted names. We choose a minimal fragment of the Ambient Logic, but the techniques we present should apply to every logic which uses Cardelli and Gordon revelation and hiding operators, and Gabbay and Pitts freshness quantifier. We start from the static fragment of ambient logic that Calcagno Cardelli and Gordon proved to be decidable. We prove that the addition of a hiding quantifier makes the logic undecidable. Hiding can be decomposed as freshness plus revelation. Quite surprisingly, freshness alone is decidable, but revelation alone is not.