Title | Decidability of a Description Logic over infinite-valued Product Logic |

Publication Type | Conference Paper |

Year of Publication | 2010 |

Authors | Cerami M [1], Esteva F [2], Bou F [3] |

Editor | Lin USattler Fa [4], Truszczynski M [5] |

Conference Name | 12th Conference on Principles of Knowledge Representation and Reasoning, KR 2010 |

Publisher | AAAI Press |

Conference Location | Toronto (Canada) |

Pagination | 203-213 |

Date Published | 10/05/2010 |

Abstract | This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i.e., the validity of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic is decidable) nor for the positive satisfiability problem, because quasi-witnessed interpretations are particularly adequate for the infinite-valued Product Logic. We give an algorithm that reduces the problem of validity (and satisfiability) of assertions in our Fuzzy Description Logic (restricted to quasi-witnessed interpretations) to a semantic consequence problem, with finite number of hypothesis, on infinite-valued propositional Product Logic. |