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**Support logic programming.**
*(English)*
Zbl 0641.68142

Summary: This article describes a support logic programming system which uses a theory of support pairs to model various forms of uncertainty. It should find application to designing expert systems and is of a query language type like Prolog. Uncertainty associated with facts and rules is represented by a pair of supports and uses ideas from Zadeh’s fuzzy set theory and Shafer’s evidence theory. A calculus is derived for such a system and various models of interpretation are given. The article provides a form of knowledge representation and inference under uncertainty suitable for expert systems and a closed world assumption is not assumed. Facts not in the knowledge base are uncertain rather than assumed to be false.

### MSC:

68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |

68T99 | Artificial intelligence |

### Keywords:

support logic programming; query language; Prolog; fuzzy set; Shafer’s evidence theory; knowledge representation; inference; expert systems
Full Text:
DOI

### References:

[1] | The Concept of Evidence, Oxford University Press, Oxford, England, 1983. |

[2] | ”An inference language based on fuzzy logic,” Proc. of Expert systems B. C. S. Special Group Conf., Cambridge, England |

[3] | ”Fuzzy reasoning: the need for blunter tools,” I. B. M Science and Uncertainty Conference papers, Science and Uncertainty, (Ed.), Science Reviews Ltd., 1983, pp. 119–137. |

[4] | and , ”CRIL-A conceptual relation inference language,” to appear. |

[5] | Baldwin, Fuzzy Sets and Systems · Zbl 0583.68048 |

[6] | and , ”Evidence theory, Fuzzy Logic and Logic Programming,” to appear. |

[7] | Baldwin, Fuzzy Sets and Systems 3 pp 193– (1980) |

[8] | Bandler, Fuzzy Sets and Systems 4 pp 13– (1980) |

[9] | and , Fuzzy Sets and Systems Theory and Applications, Academic, Orlando, FL, 1980. |

[10] | Gaines, Information Control 38 pp 154– (1978) |

[11] | and , ”New directions in the analysis and interactive elicitation of personal construct systems,” In Recent Advances in Personal Construct Theory, (Ed.), Academic, Orlando, FL, 1981. |

[12] | ”Non-monotonic reasoning using Dempster’s rule,” Proc. Nat. Conf. on Artificial Intelligence (AAAI-84), 1984, pp. 126–129. |

[13] | The Psychology of Personal Constructs, W. W. Norton, New York, 1955. |

[14] | Collected Papers, and , (Ed.), Cambridge, MA, 1933, Vol. 2. |

[15] | Induction, Blackwell, Oxford, England, 1979. |

[16] | The Range of Epistemic Logic, Aberdeen University Press, Aberdeen, Scotland, 1985. |

[17] | A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976. |

[18] | ”Negation as failure,” Rep. PM-01-85, School of Mathematics, University of Bristol, Bristol, England, 1985. |

[19] | Conceptual Structures, Addison Wesley, Reading, PA, 1984. |

[20] | and , ”On modus ponens in fuzzy logic,” Int. Symp. Multivalued Logic, 1985. |

[21] | ”On the Dempster-Shafer framework and new combination rules,” Tech. Rep. MII-504, Machine Intelligence Institute, Iona College, New Rochelle, NY, 1983. |

[22] | Zadeh, Information and Control 8 pp 339– |

[23] | Zadeh, Fuzzy Sets and Systems 1 pp 3– (1978) · Zbl 0377.04002 |

[24] | ”A theory of approximate reasoning,” In Machine Intelligence Vol.9, and (Eds.), Wiley, New York, 1979, 149–194. |

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