Towards a Reasoning Model for Context-aware Systems: Modal Logic and the Tree Model Property

@article{Limn2015TowardsAR,
  title={Towards a Reasoning Model for Context-aware Systems: Modal Logic and the Tree Model Property},
  author={Yensen Lim{\'o}n and E. B{\'a}rcenas and E. Ben{\'i}tez-Guerrero and Carmen Mezura-Godoy},
  journal={Res. Comput. Sci.},
  year={2015},
  volume={99},
  pages={9-18}
}
Modal logics forms a family of formalisms widely used as reasoning frameworks in diverse areas of computer science. Description logics and their application to the web semantic is a notable example. Also, description logics have been recently used as a reasoning model for context-aware systems. Most reasoning algorithms for modal (de- scription) logics are based on tableau constructions. In this work, we propose a reasoning (satisability) algorithm for the multi-modal Km with converse. The… Expand
Depth-First Reasoning on Trees
TLDR
This paper proposes a satisfiability algorithm for the mu-calculus extended with converse modalities and interpreted on unranked trees based on a depth-first search and proves the algorithm to be correct (sound and complete) and optimal. Expand

References

SHOWING 1-10 OF 24 REFERENCES
Automated Reasoning in Modal and Description Logics via SAT Encoding: the Case Study of K(m)/ALC-Satisfiability
TLDR
This paper starts exploring the idea of performing automated reasoning tasks in modal and description logics by encoding them into SAT, so that to be handled by state-of-the-art SAT tools; as with most previous approaches, this investigation from the satisfiability in Km. Expand
How to optimize proof-search in modal logics: new methods of proving redundancy criteria for sequent calculi
TLDR
A bottom-up decision procedure for propositional modal logic K based on the inverse method that considerably simplifies all proofs and is competitive with many state-of-the-art implementations of K. Expand
BDD-based decision procedures for the modal logic K ★
TLDR
BDD-based decision procedures for the modal logic K are described, inspired by the automata-theoretic approach, but they avoid explicit automata construction and compute certain fixpoints of a set of types — which can be viewed as an on-the-fly emptiness of the automaton. Expand
CoLoSS: The Coalgebraic Logic Satisfiability Solver
TLDR
CoLoSS, the Coalgebraic Logic Satisfiability Solver, decides satisfiability of modal formulas in a generic and compositional way and synthesises decision procedures for modular combinations of logics that include the fusion of two modal logics as a special case. Expand
Why is Modal Logic So Robustly Decidable?
  • Moshe Y. Vardi
  • Computer Science
  • Descriptive Complexity and Finite Models
  • 1996
TLDR
It is argued that the robust decidability of modal logic can be explained by the so-called tree- model property, and it is shown how the tree-model property leads to automata-based decision procedures. Expand
Modal Satisfiability via SMT Solving
TLDR
This work proposes a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers, and proves soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions. Expand
Query Reasoning on Trees with Types, Interleaving, and Counting
TLDR
This work considers the problem of query containment in the presence of type constraints for a class of regular path queries extended with counting and interleaving operators, and provides a logic-based framework supporting these operators which can be used to solve common query reasoning problems such as satisfiability and containment of queries in exponential time. Expand
Optimizing Description Logic Subsumption
TLDR
Effective optimization techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics and difficult problems in propositional modal logic can be effectively solved using the same techniques. 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
MSPASS: Subsumption Testing with SPASS
mspass is an enhancement of the rst-order theorem prover spass 17; 18; 19; 20] with a translator of modal formulae, formulae of description logics, and formulae of the relational calculus intoExpand
...
1
2
3
...