# Reasoning on expressive description logics with arithmetic constraints

@article{Brcenas2016ReasoningOE, title={Reasoning on expressive description logics with arithmetic constraints}, author={E. B{\'a}rcenas and G. Molero and Gabriela S{\'a}nchez and E. Ben{\'i}tez-Guerrero and Carmen Mezura-Godoy}, journal={2016 International Conference on Electronics, Communications and Computers (CONIELECOMP)}, year={2016}, pages={180-185} }

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 ALCQIOreg 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… Expand

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#### References

SHOWING 1-10 OF 18 REFERENCES

Graded Computation Tree Logic

- Computer Science, Mathematics
- 2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

It is proved that, although GCTL is more expressive than CTL, the satisfiability problem for GCTP remains solvable in ExpTime, and it is shown that G CTL is exponentially more succinct than graded mu-calculus. Expand

On the undecidability of logics with converse, nominals, recursion and counting

- Mathematics, Computer Science
- Artif. Intell.
- 2004

This paper improves a previous result and proves that this hybrid µ-calculus with restricted forms of graded modalities and the corresponding DL µACCIO fa are undecidable and that nested fixpoints are not necessary for undecidability. Expand

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

- Mathematics, Computer Science
- MICAI
- 2013

This work studies the fully-enriched μ-calculus for trees extended with Presburger constraints and shows that the logic is decidable in EXPTIME, achieved by the introduction of a satisfiability algorithm based on a Fischer-Ladner model construction that is able to handle binary encodings of PresBurger constraints. Expand

Reasoning in Expressive Description Logics with Fixpoints based on Automata on Infinite Trees

- Mathematics, Computer Science
- IJCAI
- 1999

This work studies a DL comprising the most general form of fixpoint constructs on concepts, all classical concept forming constructs, plus inverse roles, n-ary relations, qualified number restrictions, and inclusion assertions, and establishes the EXPTIME decidability of such logic by presenting a decision procedure based on a reduction to nonemptiness of alternating automata on infinite trees. Expand

Expressive Description Logics

- Mathematics, Computer Science
- Description Logic Handbook
- 2003

This chapter covers extensions of the basic Description Logics introduced in Chapter 2 by very expressive constructs that require advanced reasoning techniques that include general inclusion axioms, inverse roles, number restrictions, reflexive-transitive closure of roles, fixpoint constructs for recursive definitions, and relations of arbitrary arity. Expand

A Correspondence Theory for Terminological Logics: Preliminary Report

- Mathematics, Computer Science
- IJCAI
- 1991

It is proved that universal implications can be expressed within TSC, and it is shown that features correspond to deterministic programs in dynamic logic preserves decidability, although violates its finite model property. Expand

Boosting the Correspondence between Description Logics and Propositional Dynamic Logics

- Computer Science
- AAAI
- 1994

This paper derives decidability and complexity results for some of the most expressive logics appeared in the literature, and from the standpoint of PDLs, derives a general methodology for the representation of several forms of program determinism and for the specification of partial computations. Expand

Global Numerical Constraints on Trees

- Computer Science
- Log. Methods Comput. Sci.
- 2014

It is proved that the logic introduced in the present work is decidable in single exponential time even if the numerical constraints are in binary form, which implies a characterization of decidable counting extensions of XPath queries and XML schemas. Expand

The Complexity of Enriched Mu-Calculi

- Computer Science, Mathematics
- Log. Methods Comput. Sci.
- 2008

This paper identifies a family of decidable logics that are maximal (and incomparable) in expressive power in the fully enriched μ-calculus by introducing two new automata models, showing that their emptiness problems are ExpTime-complete, and reducing satisfiability in the relevant logics to these problems. Expand

Complexity of modal logics with Presburger constraints

- Computer Science, Mathematics
- J. Appl. Log.
- 2010

It is shown that EML satisfiability is only pspace -complete by designing a Ladner-like algorithm, which extends a well-known and non-trivial pspace upper bound for graded modal logic. Expand