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

### Citations

1645 |
The temporal logic of programs
- Pnueli
- 1977
(Show Context)
Citation Context ...roperty and a Fischer-Ladner construction. We show the algorithm is sound and complete, and we provide the corresponding complexity analysis. We also present some exploratory results of a preliminary implementation of the algorithm. Keywords: Modal logic, context-aware systems, reasoning. 1 Introduction Modal logics forms a family of formalism including temporal, dynamic, epistemic and description logics. These formalisms have been widely used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without ... |

450 | RACER system description
- Haarslev, Moller
- 2001
(Show Context)
Citation Context ...cond approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm perf... |

129 | Why is modal logic so robustly decidable
- Vardi
- 1997
(Show Context)
Citation Context ...tactically introduced as classical propositional logic extended with constructors for expressing modalities, such as possibility and necessity. From the seminal work of van Benthem [7], we know modal logic forms an important fragment of first order logic. The importance of this fragment comes from the associated well known and behaved computational properties, such as model checking and satisfiability. A possible explanation of this nice and robust computational behavior, provided by van Benthem [7], is that modal logic cannot distinguish bisimilar models. Another explanation comes from Vardi [20], and it concerns the tree model property of the logic. In the current work, we follow the second approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and... |

105 | A survey of context modelling and reasoning techniques,” Pervasive Mob
- Bettini, Brdiczka, et al.
- 2010
(Show Context)
Citation Context ...y used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without performance detriment [8]. Motivated by the development of expressive context aware inference systems, as an starting point, we propose in the current work a reasoning algorithm for the multimodal logic 9 Research in Computing Science 99 (2015)pp. 9–18; rec. 2015-09-30; acc. 2015-10-15 Km with converse, which can be seen as a syntactic variant of the description logic ALCI. The basic modal logic K can be syntactically introduced as... |

68 | Optimizing description logic subsumption
- Horrocks, Patel-Schneider
- 1999
(Show Context)
Citation Context ...cond approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm perf... |

52 | Knowledge, belief and time.
- Kraus, Lehmann
- 1988
(Show Context)
Citation Context ...roperty and a Fischer-Ladner construction. We show the algorithm is sound and complete, and we provide the corresponding complexity analysis. We also present some exploratory results of a preliminary implementation of the algorithm. Keywords: Modal logic, context-aware systems, reasoning. 1 Introduction Modal logics forms a family of formalism including temporal, dynamic, epistemic and description logics. These formalisms have been widely used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without ... |

45 |
Modal logic and classical logic. Bibliopolis
- BENTHEM
- 1983
(Show Context)
Citation Context ...without performance detriment [8]. Motivated by the development of expressive context aware inference systems, as an starting point, we propose in the current work a reasoning algorithm for the multimodal logic 9 Research in Computing Science 99 (2015)pp. 9–18; rec. 2015-09-30; acc. 2015-10-15 Km with converse, which can be seen as a syntactic variant of the description logic ALCI. The basic modal logic K can be syntactically introduced as classical propositional logic extended with constructors for expressing modalities, such as possibility and necessity. From the seminal work of van Benthem [7], we know modal logic forms an important fragment of first order logic. The importance of this fragment comes from the associated well known and behaved computational properties, such as model checking and satisfiability. A possible explanation of this nice and robust computational behavior, provided by van Benthem [7], is that modal logic cannot distinguish bisimilar models. Another explanation comes from Vardi [20], and it concerns the tree model property of the logic. In the current work, we follow the second approach, more precisely, we propose a satisfiability algorithm for modal logic ba... |

37 |
KRIS: knowledge representation and inference system.
- Baader, Hollunder
- 1991
(Show Context)
Citation Context ...ory results of a preliminary implementation of the algorithm. Keywords: Modal logic, context-aware systems, reasoning. 1 Introduction Modal logics forms a family of formalism including temporal, dynamic, epistemic and description logics. These formalisms have been widely used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without performance detriment [8]. Motivated by the development of expressive context aware inference systems, as an starting point, we propose in the current work a reas... |

28 | BDD-based decision procedures for the modal logic K.
- Pan, Sattler, et al.
- 2006
(Show Context)
Citation Context ...for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there are already highly optimized modal solvers successfully working in practice [13, 12], to the best of our knowledge, this is the first reasoning algorithm based on ... |

27 | Tree-based heuristics in modal theorem proving.
- Areces, Gennari, et al.
- 2000
(Show Context)
Citation Context ... [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there are already highly optimized modal solvers successfully working in practice [13, 12], to the best of our knowledge, this is ... |

15 | A decision procedure for alternation-free modal µ-calculi.
- Tanabe, Takahashi, et al.
- 2008
(Show Context)
Citation Context ...cond approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm perf... |

14 | MSPASS: Subsumption Testing with SPASS.
- Sebastiani, Hustadt, et al.
- 1999
(Show Context)
Citation Context ... [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there are already highly optimized modal solvers successfully working in practice [13, 12], to the best of our knowledge, this is ... |

13 |
How to optimize proof-search in modal logics: new methods of proving redundancy criteria for sequent calculi.
- Voronkov
- 2001
(Show Context)
Citation Context ...gic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there... |

10 | Coloss: The coalgebraic logic satisfiability solver.
- Calin, Myers, et al.
- 2009
(Show Context)
Citation Context ...ite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there are already highly... |

6 | Modality and databases.
- Fitting
- 2000
(Show Context)
Citation Context ...roperty and a Fischer-Ladner construction. We show the algorithm is sound and complete, and we provide the corresponding complexity analysis. We also present some exploratory results of a preliminary implementation of the algorithm. Keywords: Modal logic, context-aware systems, reasoning. 1 Introduction Modal logics forms a family of formalism including temporal, dynamic, epistemic and description logics. These formalisms have been widely used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without ... |

6 | Automated reasoning in modal and description logics via SAT encoding: the case study of k(m)/alc-satisfiability.
- Sebastiani, Vescovi
- 2009
(Show Context)
Citation Context ...the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2], including SMT and QBF solvers [1, 16], respectively. In [16], it is also presented a translation of modal logic formulas to types, which can be seen as an on-the-fly construction of the corresponding automaton. For the current work, we focus on the purpose-built approach. In particular, the proposed algorithm is based in the finite tree model property of modal logic. More precisely, the algorithm performs a Fischer-Ladner construction of candidate trees. Although there are already highly optimized modal solvers successfully working in practice [13, 12], to the b... |

4 | A.: Query reasoning on trees with types, interleaving, and counting.
- Barcenas, Geneves, et al.
- 2011
(Show Context)
Citation Context ...e associated well known and behaved computational properties, such as model checking and satisfiability. A possible explanation of this nice and robust computational behavior, provided by van Benthem [7], is that modal logic cannot distinguish bisimilar models. Another explanation comes from Vardi [20], and it concerns the tree model property of the logic. In the current work, we follow the second approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2]... |

4 | Efficiently deciding µ-calculus with converse over finite trees.
- Geneves, Layaıda, et al.
- 2015
(Show Context)
Citation Context |

2 |
Context-aware mobile information systems: Data management issues and opportunities.
- Benıtez-Guerrero
- 2010
(Show Context)
Citation Context ...y used as reasoning frameworks in diverse areas of computer science, such as artificial intelligence, databases, program analysis, distributed computing, etc. [17, 15, 10]. The application of description logics as knowledge representation framework (language and reasoning for ontologies) in the semantic web is a notable example [3]. In recent years, due to the well-known excellent balance between the expressive power of description logic and the computational complexity of the associated algorithms, context aware computing inference systems have been studied in the modal (descriptive) setting [8, 6]. However, current context aware systems, which are supposed to efficiently interact with a legion of context variables, still demands more expressive power without performance detriment [8]. Motivated by the development of expressive context aware inference systems, as an starting point, we propose in the current work a reasoning algorithm for the multimodal logic 9 Research in Computing Science 99 (2015)pp. 9–18; rec. 2015-09-30; acc. 2015-10-15 Km with converse, which can be seen as a syntactic variant of the description logic ALCI. The basic modal logic K can be syntactically introduced as... |

1 | Global numerical constraints on trees.
- Barcenas, Lavalle
- 2014
(Show Context)
Citation Context ...e associated well known and behaved computational properties, such as model checking and satisfiability. A possible explanation of this nice and robust computational behavior, provided by van Benthem [7], is that modal logic cannot distinguish bisimilar models. Another explanation comes from Vardi [20], and it concerns the tree model property of the logic. In the current work, we follow the second approach, more precisely, we propose a satisfiability algorithm for modal logic based on its finite tree model property. The algorithms actually builds candidate trees in the style of Fischer-Ladner [4, 5]. Moreover, the algorithm works for the modal logic extended with multimodalities Km, including converse modalities, known in description and dynamic logics as inverse roles and programs, respectively. We distinguish two types of techniques in the development of modal reasoners: purpose-built and translational. Most of purpose-built translational tools are based on tableau constructions [13, 12, 19, 11], however, there are other few methods, such as sequent calculus [21] and coalgebras [9]. In the translational methods, we may find translations to SAT solvers [18], to first order logic [14, 2]... |