## New Methods for Computing Inferences in First Order Logic (1991)

Venue: | Annals of Operations Research |

Citations: | 6 - 2 self |

### BibTeX

@ARTICLE{Hooker91newmethods,

author = {J.N. Hooker},

title = {New Methods for Computing Inferences in First Order Logic},

journal = {Annals of Operations Research},

year = {1991},

volume = {43},

pages = {479--492}

}

### OpenURL

### Abstract

Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by R. Jeroslow and a hypergraph method for datalog formulas by G. Gallo and G. Rago. We show that they are instances of two general approaches to partial instantiation, and we develop these approaches for a large decidable fragment of first order logic (the 98 fragment). 1 Introduction The last few years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods...

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Citation Context ...ombinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic =-=[1, 7, 12, 13, 20, 24, 25]-=-. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods. The pathbreaking work was done... |

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Citation Context ...years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic =-=[2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22]-=- [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribut... |

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Citation Context ...insoluble in general. In propositional logic there is a finite procedure for checking whether a formula is satisfiable: just try all assignments of truth values to the atomic propositions. But Church =-=[8]-=- proved in 1936 that first order predicate logic is undecidable, meaning that there is no such procedure that works for every formula. 2.4 Fragments Due to the undecidability of full first order logic... |

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Citation Context ...years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic =-=[2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22]-=- [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribut... |

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Citation Context ...years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic =-=[2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22]-=- [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribut... |

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Citation Context ...ng the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] =-=[23, 26]-=- and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to co... |

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Citation Context ...ombinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic =-=[1, 7, 12, 13, 20, 24, 25]-=-. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods. The pathbreaking work was done... |

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Citation Context ...his area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods. The pathbreaking work was done by R. Jeroslow =-=[21]-=-, who developed a partial instantiation method that reduces a satisfiability problem in first Working Paper 1991-11. Supported in part by the Air Force Office of Scientific Research, Grant number AFOS... |

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Citation Context ...ombinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic =-=[1, 7, 12, 13, 20, 24, 25]-=-. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods. The pathbreaking work was done... |

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Citation Context ...ng the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] =-=[23, 26]-=- and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to co... |

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Citation Context ... an inference problem) to a series of satisfiability problems in propositional logic. Optimization methods can then be applied to solving the latter problems. Shortly thereafter, G. Gallo and G. Rago =-=[9] showed ho-=-w to use hypergraphs to effect a partial instantiation method for "datalog" formulas, which are universally quantified Horn formulas in predicate logic. We will show that the work of Jeroslo... |

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