Depth-First Reasoning on Trees

@article{Limn2018DepthFirstRO,
  title={Depth-First Reasoning on Trees},
  author={Yensen Lim{\'o}n and Ismael Everardo B{\'a}rcenas Pati{\~n}o and E. Ben{\'i}tez-Guerrero and M. A. M. Nieto},
  journal={Computaci{\'o}n y Sistemas},
  year={2018},
  volume={22}
}
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… Expand
A Satisfiability Algorithm For The Mu-Calculus For Trees With Presburger Constraints
TLDR
A satisfiability algorithm for the $\mu-$calculus interpreted on tree models and extended with converse modalities and Presburger arithmetic operators, based on a breadth-first search in a Fischer-Lardner construction of tree models is described. Expand
Expressive Context Modeling with Description Logics
TLDR
This work proposes the use of an expressive description logics to model the consistency of context-aware systems and shows this expressive modeling language is capable to succinctly express complex properties, such as temporal ones. Expand
Consistency checking of attention aware systems
TLDR
This work study a formal notion of consistency in attention aware systems for the educational setting, and proposes an expressive modal logic as specification language, and a consistency checking algorithm defined in terms of the satisfiability problem of the logic. Expand
On the consistency of context-aware systems

References

SHOWING 1-10 OF 15 REFERENCES
Depth-first search satisfiability of the μ-calculus with converse over trees
TLDR
This paper proposes a satisfiability algorithm for the μ-calculus with converse interpreted on finite unranked trees based on a depth-first search, and proves the algorithm to be correct and optimal and provides an implementation, which shows significant performance improvement with respect to a known breadth- first search based algorithm. Expand
The Complexity of Enriched Mu-Calculi
TLDR
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
Towards a Reasoning Model for Context-aware Systems: Modal Logic and the Tree Model Property
TLDR
This work proposes a reasoning (satisability) algorithm for the multi-modal Km with converse based on the nite tree model property and a Fischer-Ladner construction and provides the corresponding complexity analysis. Expand
Efficiently Deciding μ-Calculus with Converse over Finite Trees
We present a sound and complete satisfiability-testing algorithm and its effective implementation for an alternation-free modal μ-calculus with converse, where formulas are cycle-free and areExpand
A decision procedure for alternation-free modal µ-calculi
TLDR
A concrete decision procedure with its complexity for AFµ enriched by features of nominals, backward modalities, and functional modalities is presented and the procedure is sound and complete for these combinations. Expand
Global Numerical Constraints on Trees
TLDR
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
On the Expressive Completeness of the Propositional mu-Calculus with Respect to Monadic Second Order Logic
TLDR
It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional Μ-calculus, which implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the Μ -calculus. Expand
MONA: Monadic Second-Order Logic in Practice
TLDR
Monadic Second-order Logic is introduced as a practical means of specifying regularity and the results show that, contrary to common beliefs, high computational complexity may be a desired feature of a specification formalism. Expand
Propositional modal logic of programs
TLDR
A fundamental propositional logical system for describing correctness, termination and equivalence of programs, and applications of the decision procedure to regular expressions, Ianov schemes, and classical systems of modal logic are introduced. Expand
Node Selection Query Languages for Trees
The study of node-selection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study ofExpand
...
1
2
...