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

In this paper we study the complexity of the model-checking problem for the tree logic introduced as the basis for the query language TQL [Cardelli and Ghelli, 2001]. We define two distinct fragments of this logic: TL containing only spatial connectives and TL containing spatial connectives and quantification. We show that the combined complexity of TL is PSPACE-hard. We also study data complexity of model-checking and show that it is linear for TL, hard for all levels of the polynomial hierarchy for TL and PSPACE-hard for the full logic. Finally we devise a polynomial space model-checking algorithm showing this way that the model-checking problem for the TQL logic is PSPACE-complete.

We introduce a simple graph logic that supports specification of Quality of Service (QoS) properties of applications. The idea is that we are not only interested in representing whether two sites are connected, but we want to express the QoS level of the connection. The evaluation of a formula in the graph logic is a value of a suitable algebraic structure, a c-semiring, representing the QoS level of the formula and not just a boolean value expressing whether or not the formula holds. We present some examples and briefly discuss the expressiveness and complexity of our logic.

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Abstract. We investigate in this paper the spatial logic TQL for querying semistructured data, represented as unranked ordered trees over an infinite alphabet. This logic consists of usual Boolean connectives, spatial connectives (derived from the constructors of a tree algebra), tree variables and a fixpoint operator for recursion. Motivated by XML-oriented tasks, we investigate the guarded TQL fragment. We prove that for closed formulas this fragment is MSO-complete. In presence of tree variables, this fragment is strictly more expressive than MSO as it allows for tree (dis)equality tests, i.e. testing whether two subtrees are isomorphic or not. We devise a new class of tree automata, called TAGED, which extends tree automata with global equality and disequality constraints. We show that the satisfiability problem for guarded TQL formulas reduces to emptiness of TAGED. Then, we focus on bounded TQL formulas: intuitively, a formula is bounded if for any tree, the number of its positions where a subtree is captured by a variable is bounded. We prove this fragment to correspond with a subclass of TAGED, called bounded TAGED, for which we prove emptiness to be decidable. This implies the decidability of the bounded guarded TQL fragment. Finally, we compare bounded TAGED to a fragment of MSO extended with subtree isomorphism tests. 1

Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its precise expressive power compared to traditional logical constructs was not previously known.

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. 1

Recently, Service Oriented Computing (SOC) has been proposed as a paradigm

Quantified µ-calculi combine the fix-point and modal operators of temporal logics with (existential and universal) quantifiers, and they allow for reasoning about the possible behaviour of individual components within a software system. In this paper we introduce a novel approach to the semantics of such calculi: we consider a sort of labelled transition systems called counterpart models as semantic domain, where states are algebras and transitions are defined by counterpart relations (a family of partial homomorphisms) between states. Then, formulae are interpreted over sets of state assignments (families of partial substitutions, associating formula variables to state components). Our proposal allows us to model and reason about the creation and deletion of components, as well as the merging of components. Moreover, it avoids the limitations of existing approaches, usually enforcing restrictions of the transition 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. The paper is rounded up with some considerations about expressiveness and decidability aspects.

Graph Logic, a query language being a sublogic of Monadic Second Order Logic is studied in [CGG02]. In the paper [DGG04] the expressiveness power of Graph Logic is examined, and it is shown, for many MSO properties, how to express them in Graph Logic. But despite of the positive examples, it is conjectured there that Graph Logic is strictly less expressive than MSO Logic.