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Expressiveness and complexity of graph logic
, 2007
"... 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 log ..."
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Cited by 15 (1 self)
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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 firstorder (FO) and monadic secondorder (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched withstyle recursion, their expressive power is sharply increased. Both are able to express PSPACEcomplete problems, although their combined complexity and data complexity still belong to PSPACE.
Decidability of Freshness, Undecidability of Revelation
 IN PROC. OF INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2003
"... 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 ..."
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Cited by 9 (2 self)
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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.
An extensional spatial logic for mobile processes
 In Proc. of CONCUR, volume 3170 of LNCS
, 2004
"... Abstract. Existing spatial logics for concurrency are intensional, in the sense that they induce an equivalence that coincides with structural congruence. In this work, we study a contextual spatial logic for the πcalculus, which lacks the spatial operators to observe emptyness, parallel composition ..."
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Cited by 9 (0 self)
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Abstract. Existing spatial logics for concurrency are intensional, in the sense that they induce an equivalence that coincides with structural congruence. In this work, we study a contextual spatial logic for the πcalculus, which lacks the spatial operators to observe emptyness, parallel composition and restriction, and only has composition adjunct and hiding. We show that the induced logical equivalence coincides with strong early bisimilarity. The proof of completeness involves the definition of nontrivial formulas, including characteristic formulas for restrictionfree processes up to bisimilarity. This result allows us to isolate the extensional core of spatial logics, decomposing spatial logics into a part that counts (given by the intensional operators) and a part that observes (given by their adjuncts). We also study how enriching the core extensional spatial logic with intensional operators affects its separative power. 1
Elimination of Quantifiers and Undecidability in Spatial Logics for Concurrency
, 2004
"... The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names ..."
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Cited by 9 (2 self)
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The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names. The logic just includes the basic spatial operators void, composition and its adjunct, and the next step modality; for the model we consider a tiny fragment of CCS. We show that this core logic can already encode its own extension with quantifiers, and modalities for actions. From this result, we derive several consequences. Firstly, we establish the intensionality of the logic, we characterize the equivalence it induces on processes, and we derive characteristic formulas. Secondly, we show that, unlike in static spatial logics, the composition adjunct adds to the expressiveness of the logic, so that adjunct elimination is not possible for dynamic spatial logics, even quantifierfree. Finally, we prove that both modelchecking and satisfiability problems are undecidable in our logic. We also conclude that our results extend to other calculi, namely the #calculus and the ambient calculus.
Adjunct elimination through games in static Ambient Logic (Extended Abstract)
 OF LNCS
, 2004
"... Spatial logics are used to reason locally about disjoint data structures. They consist of standard firstorder logic constructs, spatial (structural) connectives and their corresponding adjuncts. Lozes has shown that the adjuncts add no expressive power to a spatial logic for analysing tree structu ..."
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Cited by 6 (1 self)
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Spatial logics are used to reason locally about disjoint data structures. They consist of standard firstorder logic constructs, spatial (structural) connectives and their corresponding adjuncts. Lozes has shown that the adjuncts add no expressive power to a spatial logic for analysing tree structures, a surprising and important result. He also showed that a related logic does not have this adjunct elimination property. His proofs yield little information on the generality of adjunct elimination. We present a new proof of these results based on modelcomparison games, and strengthen Lozes ’ results. Our proof is directed by the intuition that adjuncts can be eliminated when the corresponding moves are not useful in winning the game. The proof is modular with respect to the operators of the logic, providing a general technique for determining which combinations of operators admit adjunct elimination.
Adjunct Elimination in Context Logic for Trees
"... Abstract. We study adjunctelimination results for Context Logic applied to trees, following previous results by Lozes for Separation Logic and Ambient Logic. In fact, it is not possible to prove such elimination results for the original singleholed formulation of Context Logic. Instead, we prove o ..."
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Abstract. We study adjunctelimination results for Context Logic applied to trees, following previous results by Lozes for Separation Logic and Ambient Logic. In fact, it is not possible to prove such elimination results for the original singleholed formulation of Context Logic. Instead, we prove our results for multiholed Context Logic. 1
Comparing the expressive power of Separation logic and classical logic
, 2004
"... This paper compares separation logic to a classical fragment of it. We prove that they are equally expressive, and that the separative power is obtained using only monotonic assertions. 1. ..."
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This paper compares separation logic to a classical fragment of it. We prove that they are equally expressive, and that the separative power is obtained using only monotonic assertions. 1.
Context Logic and Tree Update
"... This thesis introduces Context Logic, a novel spatial logic which was developed to allow local Hoarestyle reasoning about tree update, but which also permits reasoning about more general data update. Spatial logics have previously been used to describe properties of treelike structures (as in Ambi ..."
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This thesis introduces Context Logic, a novel spatial logic which was developed to allow local Hoarestyle reasoning about tree update, but which also permits reasoning about more general data update. Spatial logics have previously been used to describe properties of treelike structures (as in Ambient Logic) and to reason locally about dynamic updates of heaps (as in Separation Logic). However, simple adaptations of the Ambient Logic are not expressive enough to capture dynamic updates of trees. Instead, one must reason explicitly about tree contexts in order to capture updates throughout the tree. For example, a typical update removes a portion of data and replaces it by inserting new data in the same place. Context Logic allows us to reason about both the data and the place of insertion. The thesis describes the general theory of Context Logic, presents a number of extensions and applications, and shows that Context Logic is a generalisation of the Logic of Bunched Implication, the underlying theory of Separation Logic. The thesis then uses Context Logic to reason locally about tree, heap and term update languages, adapting the local reasoning framework of Separation Logic and providing a generalisation of its Frame Rule. Completeness results for these program logics are provided by deriving the weakest preconditions of the update commands from the command axioms. Finally, the thesis introduces an extended imperative update language for manipulating trees with pointers, which incorporates path queries and atomic commands that act at multiple locations. Reasoning about this raises an important point regarding the link between local reasoning and local specifications.