## Similarity-based unification: a multi-adjoint approach. Fuzzy sets and systems (2002)

Venue: | In Proc. EUSFLAT Conference in Fuzzy Logic and Technology |

Citations: | 21 - 5 self |

### BibTeX

@INPROCEEDINGS{Medina02similarity-basedunification:,

author = {Jesús Medina and Manuel Ojeda-aciego},

title = {Similarity-based unification: a multi-adjoint approach. Fuzzy sets and systems},

booktitle = {In Proc. EUSFLAT Conference in Fuzzy Logic and Technology},

year = {2002},

pages = {2004},

publisher = {Elsevier}

}

### OpenURL

### Abstract

The aim of this paper is to build a formal model for fuzzy unification in multi-adjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of first-order logic with equality.

### Citations

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(Show Context)
Citation Context ...tional model, in a single step. The reductant property is defined in [7] so that a single rule in the program computes the supremum stated above (which is a generalisation of the concept of reductant =-=[5]-=-): The proof of the completeness theorem follows from the fact that the least fix-point is also the least model of a program. Theorem 1 Assume a MA program P with the reductant property such that T L ... |

89 | The Semantic Web: the roles of XML and RDF - Decker, Melnik, et al. - 2000 |

53 | Non–commutative residuated lattices - Ward, Dilworth - 1939 |

44 | Monotonic and residuated logic programs
- Damásio, Pereira
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Citation Context ...rally leads to the allowance of several adjoint pairs in the lattice of truth-values. This idea is used in [6] to introduce MA logic programs as an extension of monotonic logic programs, presented in =-=[2, 3]-=- so that it is possible to use a number of different implications in the rules of our programs. The semantics of generalized logic programs requires a notion of consequence (implication) which satisfi... |

39 | Multi-adjoint logic programming with continuous semantics
- Medina, Ojeda-Aciego, et al.
- 2001
(Show Context)
Citation Context ...joint (MA) logic programming Our approach to fuzzy unification is based on a theory of fuzzy logic programming with crisp unification constructed on the multi-adjoint framework recently introduced in =-=[7, 6]-=-. We recall definitions of declarative and procedural semantics of multi-adjoint logic programming and show how its soundness and completeness, and especially the fixpoint theorem and the minimal mode... |

22 | A procedural semantics for multi-adjoint logic programming
- Medina, Ojeda-Aciego, et al.
- 2001
(Show Context)
Citation Context ...joint (MA) logic programming Our approach to fuzzy unification is based on a theory of fuzzy logic programming with crisp unification constructed on the multi-adjoint framework recently introduced in =-=[7, 6]-=-. We recall definitions of declarative and procedural semantics of multi-adjoint logic programming and show how its soundness and completeness, and especially the fixpoint theorem and the minimal mode... |

19 | Hybrid probabilistic logic programs as residuated logic programs
- Damásio, Pereira
- 2000
(Show Context)
Citation Context ...rally leads to the allowance of several adjoint pairs in the lattice of truth-values. This idea is used in [6] to introduce MA logic programs as an extension of monotonic logic programs, presented in =-=[2, 3]-=- so that it is possible to use a number of different implications in the rules of our programs. The semantics of generalized logic programs requires a notion of consequence (implication) which satisfi... |

19 |
Fuzzy logic programming. Fuzzy sets and systems
- Vojtáˇs
(Show Context)
Citation Context ... satisfies a generalized modus ponens rule. It is natural to look for a semantic basis as a common denominator of the residuated lattices and fairly general conjunctors and their adjoints, as used in =-=[8]-=-. The main point in the extension to a more general setting, in which different implications (and several modus ponens-like inference rules) are used, naturally leads to considering several adjoint pa... |

16 | A formula for incorporating weights into scoring rules - FAGIN, L |

10 |
Similarity-based unification
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(Show Context)
Citation Context ...1,y1) &P ··· &P sn(xn,yn) s(f(x1,...,xn),f(y1,...,yn)) ←i s1(x1,y1) &P ··· &P sn(xn,yn) it is possible to get computed answers with similarity match in unification. In contrast, the approach taken in =-=[4]-=- is based on fuzzy set theory and computing something like the degree of being a singleton. They are restricted to max-min connectives and we argue that similarity has to be coupled by product semanti... |

6 |
Likelog: a logic programming language for flexible data retrieval
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- 1999
(Show Context)
Citation Context ...omputed answer (δ, θ ′ ) such that λn0 � δ and θ′ is more general than θ. Similarity-based unification A lot of research has been done in the field of unification based on similarities, for instance, =-=[1]-=-sstarts from unification based on similarity to derive a logic programming system, thoroughly relying on similarity, one of its principal features being the allowance of flexible information retrieval... |

4 | Multi-adjoint logic programming: a neural net approach - Medina, Mérida-Casermeiro, et al. - 2002 |

2 |
Lukasiewicz logic programming based on fuzzy equality
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- 1996
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Citation Context ...ic programming system, thoroughly relying on similarity, one of its principal features being the allowance of flexible information retrieval in deductive data bases. On the other hand, the purpose of =-=[9]-=- is to investigate the use of similarities as the basis for unification and resolution in logic programming. As a result, a well-founded semantical method to incorporate linguistic variables into logi... |

2 | What’s next in database - Jeffery - 1999 |

1 | Low retrieval remote querying dialogue with fuzzy conceptual, syntactical and linguistical unification - Kriˇsko, Marcinˇsák, et al. - 1998 |

1 | Algoritmy v oblasti získavania informácii - Lencses - 2001 |