Depth-first search satisfiability of the μ-calculus with converse over trees

Limón, Yensen; Bárcenas, Everardo; Benítez–Guerrero, Edgard; Medina, Ma. Auxilio

doi:10.1109/conielecomp.2017.7891827

Cited by 1 publication

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“…The propositional µ-calculus is a modal logic with least and fixed-point operators, expressively corresponding to the monadic second order logic MSO [9]. This logic is known to subsume many temporal, program and description logics such as Preliminary results were presented in [11,12] the Linear Temporal Logic LTL, the Propositional Dynamic Logic PDL, the Computation Tree Logic CTL and ALC reg , which is an expressive description logic with negation and regular roles [4]. Due to its expressive power and nice computational properties, the µ-calculus has been extensively used as a reasoning framework in a wide range of domains, such as program verification, knowledge representation and concurrent pervasive systems [4].…”

Section: Introductionmentioning

confidence: 99%

Depth-First Reasoning on Trees

Priego¹,

Patiño²,

Guerrero³

et al. 2018

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The µ-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 µ-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 µ-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.

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