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We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence.
A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (datum) from an infinite set, where the latter can only be compared for equality. The article considers alternating automata on dat
We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply add
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations o
We investigate tree-automatic well-founded trees. Using Delhommes decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. Moreover, we make a step tow
Proposition algebra is based on Hoares conditional connective, which is a ternary connective comparable to if-then-else and used in the setting of propositional logic. Conditional statements are provided with a simple semantics that is based on evalu