Axiomatizations for downward XPath on Data Trees

We give sound and complete axiomatizations for XPath with data tests by "equality" or "inequality", and containing the single "child" axis. This data-aware logic predicts over data trees, which are tree-like structures whose every node contains a label from a finite alphabet and a data value from an infinite domain. The language allows us to compare data values of two nodes but cannot access the data values themselves (i.e. there is no comparison by constants). Our axioms are in the style of equational logic, extending the axiomatization of data-oblivious XPath, by B. ten Cate, T. Litak and M. Marx. We axiomatize the full logic with tests by "equality" and "inequality", and also a simpler fragment with "equality" tests only. Our axiomatizations apply both to node expressions and path expressions. The proof of completeness relies on a novel normal form theorem for XPath with data tests

Data Storage Interpretation of Labeled Modal Logic

We introduce reference structures -- a basic mathematical model of a data organization capable to store and utilize information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming languages is presented as an example of a reference structure building. 1 Introduction We suggest to interpret a labeled modal formula [[m]]A as "memory cell m stores sentence A" and to treat propositional variables as names of the cell contents. The Annals of Pure and Applied Logic, v. 78, pp. 57-71, 1996 y The research described in this publication was made possible in part by Grant No.NFQ..