## A Semantics for Fuzzy Logic (1997)

Venue: | Soft Computing |

Citations: | 7 - 0 self |

### BibTeX

@ARTICLE{Paris97asemantics,

author = {J. B. Paris},

title = {A Semantics for Fuzzy Logic},

journal = {Soft Computing},

year = {1997},

volume = {1},

pages = {143--147}

}

### OpenURL

### Abstract

We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is used in two separate ways (at least). One is where `truth values' are intended to stand for measures of belief (or condence, or certainty of some sort) and the expression `Fuzzy Logic' is taken as a synonym for the assumption that belief values are truth functional. That is, if w() denotes an agent's belief value (on the usual scale [0; 1]) for 2 SL, where SL is the set of sentences from a nite propositional language L built up using the connectives :; ^; _ (we shall consider implication later), then w satises w(:) = F: (w()); w( ^ ) = F^ (w(); w()); w( _ ) = F_ (w(); w()); (1) for some xed functions F: : [0; 1] ! [0; 1] and F^ ; F_ : [0; 1] 2 ! [0; 1]; where ; 2 SL. Two p...

### Citations

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Citation Context ...unds of computational simplicity (see [9], [10],[11]). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this paper, is as the logic(s) of vagueness, see =-=[12]-=-, [13]. To elaborate, it seems to be the case that we, as examples of so called intelligent agents, can give (subjective) degrees of truth to assertions involving vague predicates. Thus, for example a... |

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Citation Context ...f computational simplicity (see [9], [10],[11]). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this paper, is as the logic(s) of vagueness, see [12], =-=[13]-=-. To elaborate, it seems to be the case that we, as examples of so called intelligent agents, can give (subjective) degrees of truth to assertions involving vague predicates. Thus, for example an agen... |

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Citation Context ... yg, to be dened, and, in the current terminology, it is this version which is now frequently referred to as ` Lukasiewicz Logic'. At a somewhat later date (1932) Godel also introduced a logic (see [2=-=-=-]) with conjunction and disjunction as in (2) (but with a dierent negation). The earliest clear use of (2), without also implication, appears to have been by Chang and Lee in [3] in 1971. For the conn... |

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Citation Context ...Mycin (see [6]) and is rather widespread in theoretical expert systems (although not, apparently, in genuine working systems, see [7]). Its use in this context is dicult to justify (see, for example, =-=[8]-=- p53), except possibly on the pragmatic grounds of computational simplicity (see [9], [10],[11]). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this p... |

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Citation Context ...s of w so that the the schema (2) (the most popular choice of all as we judge it) is satised. It is the purpose of this short note to propose one such semantics. [We refer the reader to [14],[15] 1 ,[=-=16]-=-,[18],[11],[19] for alternate proposals.] We should, perhaps, point out at this stage that amongst some of those close to the pulse of vagueness there is a viewpoint that no such semantics are necessa... |

69 | The paradoxical success of fuzzy logic
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Citation Context ...he use of `Fuzzy Logic' in the context of belief values dates back to Mycin (see [6]) and is rather widespread in theoretical expert systems (although not, apparently, in genuine working systems, see =-=[7]-=-). Its use in this context is dicult to justify (see, for example, [8] p53), except possibly on the pragmatic grounds of computational simplicity (see [9], [10],[11]). A second way that the expression... |

37 |
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Citation Context ...he values of w so that the the schema (2) (the most popular choice of all as we judge it) is satised. It is the purpose of this short note to propose one such semantics. [We refer the reader to [14],[=-=15]-=- 1 ,[16],[18],[11],[19] for alternate proposals.] We should, perhaps, point out at this stage that amongst some of those close to the pulse of vagueness there is a viewpoint that no such semantics are... |

35 |
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Citation Context ... Product Logic (less its implication), see [4]. [For an excellent survey of Fuzzy Logics we refer the reader to [5].] The use of `Fuzzy Logic' in the context of belief values dates back to Mycin (see =-=[6]-=-) and is rather widespread in theoretical expert systems (although not, apparently, in genuine working systems, see [7]). Its use in this context is dicult to justify (see, for example, [8] p53), exce... |

28 | A complete many-valued logic with product conjunction, Archive for
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(Show Context)
Citation Context ...pears to have been by Chang and Lee in [3] in 1971. For the connectives conjunction and disjunction (but not negation) the second schema, (3), corresponds to Product Logic (less its implication), see =-=[4]-=-. [For an excellent survey of Fuzzy Logics we refer the reader to [5].] The use of `Fuzzy Logic' in the context of belief values dates back to Mycin (see [6]) and is rather widespread in theoretical e... |

18 |
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(Show Context)
Citation Context ... to the values of w so that the the schema (2) (the most popular choice of all as we judge it) is satised. It is the purpose of this short note to propose one such semantics. [We refer the reader to [=-=14]-=-,[15] 1 ,[16],[18],[11],[19] for alternate proposals.] We should, perhaps, point out at this stage that amongst some of those close to the pulse of vagueness there is a viewpoint that no such semantic... |

13 |
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(Show Context)
Citation Context ...troduced a logic (see [2]) with conjunction and disjunction as in (2) (but with a dierent negation). The earliest clear use of (2), without also implication, appears to have been by Chang and Lee in [=-=3]-=- in 1971. For the connectives conjunction and disjunction (but not negation) the second schema, (3), corresponds to Product Logic (less its implication), see [4]. [For an excellent survey of Fuzzy Log... |

9 | A new criterion for comparing fuzzy logics for uncertain reasoning
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(Show Context)
Citation Context ..., apparently, in genuine working systems, see [7]). Its use in this context is dicult to justify (see, for example, [8] p53), except possibly on the pragmatic grounds of computational simplicity (see =-=[9]-=-, [10],[11]). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this paper, is as the logic(s) of vagueness, see [12], [13]. To elaborate, it seems to be ... |

7 | Embedding Logics into Product Logic
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(Show Context)
Citation Context ..., indirect, route by which this Logic might possibly be furnished with some such semantics is by using the embedding ofsLukasiewicz Logic into Product Logic `with too small truth degrees' as given in =-=[20]-=-, although our endeavours to date along these lines have again been unconvincing. [In [18] Mundici does exhibit an intriguing semantics for (k + 2)-valuedsLukasiewicz Logic, although it appears unrela... |

4 |
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(Show Context)
Citation Context ...w so that the the schema (2) (the most popular choice of all as we judge it) is satised. It is the purpose of this short note to propose one such semantics. [We refer the reader to [14],[15] 1 ,[16],[=-=18]-=-,[11],[19] for alternate proposals.] We should, perhaps, point out at this stage that amongst some of those close to the pulse of vagueness there is a viewpoint that no such semantics are necessary, j... |

4 |
Vagueness and Utility: The Semantics of
- Parikh
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(Show Context)
Citation Context ...the the schema (2) (the most popular choice of all as we judge it) is satised. It is the purpose of this short note to propose one such semantics. [We refer the reader to [14],[15] 1 ,[16],[18],[11],[=-=19]-=- for alternate proposals.] We should, perhaps, point out at this stage that amongst some of those close to the pulse of vagueness there is a viewpoint that no such semantics are necessary, just as no ... |

3 |
A Note on Probability versus TruthFunctionality
- Wilmers, Paris, et al.
- 1994
(Show Context)
Citation Context ...arently, in genuine working systems, see [7]). Its use in this context is dicult to justify (see, for example, [8] p53), except possibly on the pragmatic grounds of computational simplicity (see [9], =-=[10]-=-,[11]). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this paper, is as the logic(s) of vagueness, see [12], [13]. To elaborate, it seems to be the ca... |

1 |
Fuzzy logic from the logical point of view, SOFSEM'95: Theory and Practice of Informatics
- Hajek
- 1995
(Show Context)
Citation Context ...es conjunction and disjunction (but not negation) the second schema, (3), corresponds to Product Logic (less its implication), see [4]. [For an excellent survey of Fuzzy Logics we refer the reader to =-=[5]-=-.] The use of `Fuzzy Logic' in the context of belief values dates back to Mycin (see [6]) and is rather widespread in theoretical expert systems (although not, apparently, in genuine working systems, ... |

1 |
A New Criterion for Comparing Fuzzy Logics, submitted to the International Journal of Approximate Reasoning
- Bennett, Paris, et al.
(Show Context)
Citation Context ...ly, in genuine working systems, see [7]). Its use in this context is dicult to justify (see, for example, [8] p53), except possibly on the pragmatic grounds of computational simplicity (see [9], [10],=-=[11]-=-). A second way that the expression `Fuzzy Logic(s)' is used, and the one which will concern us in this paper, is as the logic(s) of vagueness, see [12], [13]. To elaborate, it seems to be the case th... |

1 |
A Voting Mechanism for Fuzzy Logic, submitted to International Journal of Approximate Reasoning
- Lawry
(Show Context)
Citation Context ...for 2 SL the agent's set of arguments for ; + , and set of arguments against ; , are assumed to satisfy the following for somesxed,snite, non-empty, 1 In connection with these papers see also [17] 2 set T of worlds 2 : (1) For 2 L (i.e. a propositional variable) + = f V 2 T j V () = 1 (i:e: true) g and = f V 2 T j V () = 0 (i:e: false) g. (2) (:) + = ; (:) = + : (3) ( ^) + is... |