Expressive Reasoning on Tree Structures: Recursion, Inverse Programs, Presburger Constraints and Nominals

Bárcenas, Everardo; Lavalle, Jesús

doi:10.1007/978-3-642-45114-0_7

Cited by 10 publications

(13 citation statements)

References 9 publications

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“…Actually, it was proven an EXPTIME bound for the fully enriched μ-calculus for trees. Generalizations of this result were later reported in [14], [15]. More precisely, EXPTIME bounds were also proven for the fully enriched μ-calculus for trees with generalizations of graded modalities, in [15] for global counting, and in [14] with Presburger constraints.…”

Section: A Related Workmentioning

confidence: 73%

“…More precisely, EXPTIME bounds were also proven for the fully enriched μ-calculus for trees with generalizations of graded modalities, in [15] for global counting, and in [14] with Presburger constraints. In the current work, we import the EXPTIME reasoning bounds of μALCPIO from the μ-calculus as presented in [14]. This is achieved vía a polynomial reduction.…”

Section: A Related Workmentioning

confidence: 95%

“…Other expressive logics with counting (arithmetic) constraints have been recently studied [10], [11], [9], [12], [13], [14], [15]. In [10], basic modal logic extended with Presburger constraints is shown to be in PSPACE.…”

Section: A Related Workmentioning

confidence: 98%

“…Theorem 4 (μ-calculus complexity [14]). Decidability of the enriched μ-calculus for trees with Presburger constraints is in EXPTIME.…”

Section: A Syntax and Semanticsmentioning

confidence: 99%

“…In this section, we give a description of the enriched μ-calculus for trees with Presburger constraints as originally introduced in [14]. The enriched μ-calculus is an expressive modal logic with least and greatest fixed points and inverse modalities.…”

Section: μ-Calculus With Presburger Constraintsmentioning

confidence: 99%

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Reasoning on expressive description logics with arithmetic constraints

Bárcenas

Molero

Sanchez

et al. 2016

2016 International Conference on Electronics, Communications and Computers (CONIELECOMP)

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Description logics (DL) is a well-known knowledge representation formalism. DL have been applied as reasoning framework in diverse domains, including the Semantic Web and Context-Aware Systems. It is an open question whether or not the expressive description logic ALCQIO reg is decidable. This logic is equipped with negation, conjunction, regular roles, inverse roles, nominals and qualified number restrictions. In this paper, we show this logic is decidable when interpreted over tree models. Moreover, it is shown that μALCPIO, which is known to be undecidable and that subsumes ALCQIO reg , is in EXPTIME in the case of tree models. μALCPIO generalizes regular roles with fixed-point constructors, and qualified number restrictions with arithmetic constraints. This EXPTIME bound holds even if the arithmetic constraints are coded in binary. Furthermore, we show that knowledge base reasoning, TBoxes and ABoxes, can also be decided in EXPTIME. These results are achieved via a polynomial reduction to the satisfiability problem of the propositional modal μ-calculus extended with Presburger arithmetic constraints interpreted over tree models.

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Section: A Related Workmentioning

confidence: 73%

Section: A Related Workmentioning

confidence: 95%

Section: A Related Workmentioning

confidence: 98%

“…Theorem 4 (μ-calculus complexity [14]). Decidability of the enriched μ-calculus for trees with Presburger constraints is in EXPTIME.…”

Section: A Syntax and Semanticsmentioning

confidence: 99%

Section: μ-Calculus With Presburger Constraintsmentioning

confidence: 99%

See 3 more Smart Citations

Reasoning on expressive description logics with arithmetic constraints

Bárcenas

Molero

Sanchez

et al. 2016

2016 International Conference on Electronics, Communications and Computers (CONIELECOMP)

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Reasoning with Global Assumptions in Arithmetic Modal Logics

Kupke

Pattinson

Schröder

2015

Fundamentals of Computation Theory

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Abstract. We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.

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