## Modal Semantics for Knowledge Bases Dealing with Vague Concepts (1998)

Venue: | Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR-98 |

Citations: | 11 - 5 self |

### BibTeX

@INPROCEEDINGS{Bennett98modalsemantics,

author = {Brandon Bennett},

title = {Modal Semantics for Knowledge Bases Dealing with Vague Concepts},

booktitle = {Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR-98},

year = {1998},

pages = {234--244},

publisher = {Morgan Kaufman}

}

### OpenURL

### Abstract

The paper investigates the characterisation of vague concepts within the framework of modal logic. This work builds on the supervaluation approach of Fine and exploits the idea of a precisification space. A simple language is presented with two modalities: a necessity operator and an operator `it is unequivocal that' which is used to articulate the logic of vagueness. Both these operators obey the schemas of the logic S5. I show how this language can be used to represent logical properties of vague predicates which have a variety of possible precise interpretations. I consider the use within KR systems of number of different entailment relations that can be specified for this language. Certain vague predicates (such as `tall') may be indefinite even when there is no ambiguity in meaning. These can be accounted for by means of a three-valued logic, incorporating a definiteness operator. I also show the relationship between observable quantities (such as height) and vague predicates (su...

### Citations

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(Show Context)
Citation Context ...ENT APPROACH TO PREVIOUS WORK In computer science the approaches to vagueness that have received the most attention are those based on multi-valued logics (/Lukasiewicz and Tarski 1930). Fuzzy logic (=-=Zadeh 1965-=-, Zadeh 1975, Goguen 1969, Dubois and Prade 1988) can be regarded as a generalised multi-valued logic. An extensive discussions of the pros and cons of fuzzy logic can be found in (Elkan 1993). In acc... |

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Citation Context ...anguages (van Frassen 1968, van Frassen 1969). be important and it will be useful to explicitly distinguish them both syntactically and semantically. To do this I employ the modal logic S5 (see e.g. (=-=Hughes and Cresswell 1969-=-)). This enables theoretical information to be represented by formulae of the formsOE (factual formulae will not contain modal operators). In order to articulate the logic of vagueness I introduce int... |

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Citation Context ... easy for contradictions to occur because of slight differences in the intended meaning of different occurrences of predicates in a set of axioms. In the construction of large axiomatised ontologies (=-=Guha and Lenat 1990-=-) this problem is especially acute. I believe that a logical treatment of vagueness can be particularly useful in preventing inconsistency arising in this way. Similar problems also occur when one att... |

123 | Two-Dimensional Modal Logic - Segerberg - 1973 |

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Citation Context ...e idea is that vague expressions are associated not with a single extension but with a set of different possible extensions. This can be modelled by means of a Kripke-style possible worlds semantics (=-=Kripke 1959-=-). In a recent book by Williamson (1994), it is argued that vagueness should be regarded as a epistemic phenomenon and proposes a modal treatment of vagueness rather different from that of Fine. This ... |

91 |
An introduction to possibilistic and fuzzy logics
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(Show Context)
Citation Context ...uter science the approaches to vagueness that have received the most attention are those based on multi-valued logics (/Lukasiewicz and Tarski 1930). Fuzzy logic (Zadeh 1965, Zadeh 1975, Goguen 1969, =-=Dubois and Prade 1988-=-) can be regarded as a generalised multi-valued logic. An extensive discussions of the pros and cons of fuzzy logic can be found in (Elkan 1993). In accord with Elkan, I suggest that fuzzy logic may b... |

73 |
The Logic of Inexact Concepts
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(Show Context)
Citation Context ... WORK In computer science the approaches to vagueness that have received the most attention are those based on multi-valued logics (/Lukasiewicz and Tarski 1930). Fuzzy logic (Zadeh 1965, Zadeh 1975, =-=Goguen 1969-=-, Dubois and Prade 1988) can be regarded as a generalised multi-valued logic. An extensive discussions of the pros and cons of fuzzy logic can be found in (Elkan 1993). In accord with Elkan, I suggest... |

70 | The paradoxical success of fuzzy logic
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(Show Context)
Citation Context ...y logic (Zadeh 1965, Zadeh 1975, Goguen 1969, Dubois and Prade 1988) can be regarded as a generalised multi-valued logic. An extensive discussions of the pros and cons of fuzzy logic can be found in (=-=Elkan 1993-=-). In accord with Elkan, I suggest that fuzzy logic may be an appropriate formalism for modelling the relation between continuous valued observables and the meanings of vague qualitative predicates; h... |

65 |
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(Show Context)
Citation Context ...:sSOE n ) ! S/ ffl OE 1 ; : : : ; OE n j= co\Gammareliable / iff j= S5U S(OE 1s: : :sOE n ) ! U/ ffl OE 1 ; : : : ; OE n j= co\Gammas\Gammareliable / iff j= S5U S(OE 1s: : :sOE n ) ! S/ Philosophers (=-=Fine 1975-=-, Williamson 1994) have been most concerned with the first two definitions of validity. So-called `local' validity means that under-any interpretation where the premisses are true the conclusion is al... |

42 |
Untersuchungen über den Aussagenkalkül. Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie
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Citation Context ...e of KR&R systems. 1.1 RELATION OF THE PRESENT APPROACH TO PREVIOUS WORK In computer science the approaches to vagueness that have received the most attention are those based on multi-valued logics (/=-=Lukasiewicz and Tarski 1930-=-). Fuzzy logic (Zadeh 1965, Zadeh 1975, Goguen 1969, Dubois and Prade 1988) can be regarded as a generalised multi-valued logic. An extensive discussions of the pros and cons of fuzzy logic can be fou... |

32 |
The EGG/YOLK reliability hierarchy : Semantic data integration using sorts with prototypes
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(Show Context)
Citation Context ...ent of vagueness can be particularly useful in preventing inconsistency arising in this way. Similar problems also occur when one attempts to combine information from two or more different databases (=-=Lehmann and Cohn 1994-=-). In this paper I shall show that by a suitable logical treatment of vagueness it is possible to safely combine data and axioms where the meanings of predicates may vary from instance to instance. Mo... |

13 |
Vagueness: An Investigation into Natural Languages and the Sorites Paradox
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(Show Context)
Citation Context ...TES ARGUMENT I now consider the famous sorites paradox which is perhaps the best known example of the way that vagueness seems to defy logical analysis. Detailed accounts may be found in (Black 1970, =-=Burns 1991-=-, Williamson 1994). The original example of this paradox concerns the question of how many grains of sand constitute a `heap' (`sorites' is Greek for heap) but I shall consider the directly analogous ... |

11 | A mereological approach to representing spatial vagueness
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(Show Context)
Citation Context ...n from AI researchers (see e.g. (Shafer and Pearl 1990)). 2 The logic of vague objects is likely to be very different from that of vague predicates. A theory of vague spatial objects can be found in (=-=Cohn and Gotts 1996-=-). 2 PRECISIFICATION SPACES AND SUPERVALUATIONS The supervaluation theory of vagueness proposed by Fine (1975) is based on the idea that expressions of a language which includes vague expressions can ... |

8 |
Logic and Lexicon The Semantics of the Indefinite
- Pinkal
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(Show Context)
Citation Context ... is indefinite in every sense. This motivates the construction of a three-valued precisification semantics. 3.1 THREE-VALUED PRECISIFICATION SPACES In a three-valued precisification model (Fine 1975, =-=Pinkal 1995-=-), a precisification is associated with a function mapping each atomic predicate and each tuple of arguments to a value in the set ft; f; ig (true, false and indefinite). A precisification which only ... |

3 |
Vagueness, The problems of philosophy
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(Show Context)
Citation Context ... S/ ffl OE 1 ; : : : ; OE n j= co\Gammareliable / iff j= S5U S(OE 1s: : :sOE n ) ! U/ ffl OE 1 ; : : : ; OE n j= co\Gammas\Gammareliable / iff j= S5U S(OE 1s: : :sOE n ) ! S/ Philosophers (Fine 1975, =-=Williamson 1994-=-) have been most concerned with the first two definitions of validity. So-called `local' validity means that under-any interpretation where the premisses are true the conclusion is also true. However,... |

1 |
Reasoning with loose concepts, Margins of Precision
- Black
- 1970
(Show Context)
Citation Context ...2.5 THE SORITES ARGUMENT I now consider the famous sorites paradox which is perhaps the best known example of the way that vagueness seems to defy logical analysis. Detailed accounts may be found in (=-=Black 1970-=-, Burns 1991, Williamson 1994). The original example of this paradox concerns the question of how many grains of sand constitute a `heap' (`sorites' is Greek for heap) but I shall consider the directl... |

1 | Presupposition, implication and self-reference - Frassen - 1968 |

1 | Presupposition, supervaluations and free logic - Frassen - 1969 |