Abstract

LIMON, Yensen; BARCENAS, Everardo; BENITEZ-GUERRERO, Edgard  and  MEDINA, María Auxilio. Depth-First Reasoning on Trees. Comp. y Sist. [online]. 2018, vol.22, n.1, pp.189-201. ISSN 2007-9737.  https://doi.org/10.13053/cys-22-1-2776.

The $\mu$-calculus is an expressive modal logic with least and greatest fixed-point operators. This formalism encompasses many temporal, program and description logics, and it has been widely applied in a broad range of domains, such as, program verification, knowledge representation and concurrent pervasive systems. In this paper, we propose a satisfiability algorithm for the $\mu$-calculus extended with converse modalities and interpreted on unranked trees. In contrast with known satisfiability algorithms, our proposal is based on a depth-first search. We prove the algorithm to be correct (sound and complete) and optimal. We also describe an implementation. The extension of the $\mu$-calculus with converse modalities allows to efficiently characterize standard reasoning problems (emptiness, containment and equivalence) of XPath queries. We also describe several query reasoning experiments, which shows our proposal to be competitive in practice with known implementations.

Keywords : Calculus; automated reasoning; depth-first search; XPath.

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