## Some Uses of Higher-Order Logic in Computational Linguistics (1986)

Venue: | In 24st Annual Meeting of the Association for Computational Linguistics |

Citations: | 23 - 10 self |

### BibTeX

@INPROCEEDINGS{Miller86someuses,

author = {Dale A. Miller and Gopalan Nadathur},

title = {Some Uses of Higher-Order Logic in Computational Linguistics},

booktitle = {In 24st Annual Meeting of the Association for Computational Linguistics},

year = {1986},

pages = {247--255}

}

### Years of Citing Articles

### OpenURL

### Abstract

Consideration of the question of meaning in the framework of linguistics often requires an allusion to sets and other higher-order notions. The traditional approach to representing and reasoning about meaning in a computational setting has been to use knowledge representation systems that are either based on first-order logic or that use mechanisms whose formal justifications are to be provided after the fact. In this paper we shall consider the use of a higher-order logic for this task. We first present a version of definite clauses (positive Horn clauses) that is based on this logic. Predicate and function variables may occur in such clauses and the terms in the language are the typed -terms. Such term structures have a richness that may be exploited in representing meanings. We also describe a higher-order logic programming language, called Prolog, which represents programs as higher-order definite clauses and interprets them using a depth-first interpreter. A virtue of this languag...

### Citations

847 |
A formulation of the simple theory of types
- Church
- 1940
(Show Context)
Citation Context ...ng an example of determining pronoun reference. 2. Higher-Order Logic The higher-order logic we study here, called T , can be thought of as being a subsystem of either Church's Simple Theory of Types =-=[5]-=- or of Montague's intensional logic IL [6]. Unlike Church's or Montague's logics, T is very weak because it assumes no axioms regarding 2 extensionality, definite descriptions, infinity, choice, or po... |

582 | An overview of the KL-ONE knowledge representation system
- Brachman, Schmolze
- 1985
(Show Context)
Citation Context ...Knowledge Representation We now consider the question of how a higher-order logic might be used for the task of representing knowledge. Traditionally, certain network based formalisms, such as KL-ONE =-=[4]-=-, have been described for this purpose. Such formalisms use nodes and arcs in a network to encode knowledge, and provide algorithms that operate on this network in order to perform inferences on the k... |

342 |
Definite clause grammars for language analysis - a survey of the formalism and a comparison with augmented transition networks
- Pereira, Warren
- 1980
(Show Context)
Citation Context ...man" to the logical form 8x(man(x) oe 9y(woman(y)sloves(x; y))) which in our context will be represented by the -term (all X"(man X =? (some Y"(woman Y & loves X Y)))) A higher-order ve=-=rsion of a DCG [10]-=- for performing this task is provided below. This DCG draws on the spirit of Montague Grammars. (See [11] for a similar example.) sentence (P1 P2) --? np P1, vp P2, [.]. np (P1 P2) --? determ P1, nom ... |

180 |
The tractability of subsumption in framebased description languages
- Brachman, Levesque
- 1984
(Show Context)
Citation Context ... :- subsume (restr R C) D, related R V U, isa D V. isa C U :- subsume C D, isa D U. The resulting first-order program is isomorphic to the original, higher-order program. The subsumption algorithm in =-=[3]-=- is essentially the one specified by the clauses that define subsume. There are two important points to make regarding this program, however. First, to correctly specify its meaning, one needs to deve... |

169 |
A unification algorithm for typed -calculus
- Huet
- 1975
(Show Context)
Citation Context ...in higher-order logic than in first-order logic as claimed in the last point, the nature of proofs in higherorder logic is far from mysterious. For example, higherorder resolution [1] and unification =-=[8]-=- has been developed, and based on these principles, several theorem provers for various higher-order logics (see [2] and its references) have been built and tested. The experience with such systems sh... |

106 | Resolution in Type Theory
- Andrews
- 1971
(Show Context)
Citation Context ... on theorem proving in higher-order logic than in first-order logic as claimed in the last point, the nature of proofs in higherorder logic is far from mysterious. For example, higherorder resolution =-=[1]-=- and unification [8] has been developed, and based on these principles, several theorem provers for various higher-order logics (see [2] and its references) have been built and tested. The experience ... |

3 |
Eve Longini Cohen, Frank Pfenning, "Automating HigherOrder Logic," in Automated Theorem Proving: After 25 Years, edited by
- Andrews, Miller
- 1984
(Show Context)
Citation Context ...gic is far from mysterious. For example, higherorder resolution [1] and unification [8] has been developed, and based on these principles, several theorem provers for various higher-order logics (see =-=[2]-=- and its references) have been built and tested. The experience with such systems shows that theorem proving in such a logic is difficult. It is not clear, however, that the difficulty is inherent in ... |

3 |
Using -calculus to represent meanings in logic grammars. In 21st Annual Meeting of the Association for Computational Linguistics
- Warren
- 1983
(Show Context)
Citation Context ...by the -term (all X"(man X =? (some Y"(woman Y & loves X Y)))) A higher-order version of a DCG [10] for performing this task is provided below. This DCG draws on the spirit of Montague Gramm=-=ars. (See [11] for a similar -=-example.) sentence (P1 P2) --? np P1, vp P2, [.]. np (P1 P2) --? determ P1, nom P2. np P"(P X) --? propernoun X. nom P --? noun P. nom X"(P1 X & P2 X) --? noun P1, relcl P2. vp X"(P2 (P... |

1 |
Gopalan Nadathur, "Higher-order Logic Programming
- Miller
- 1986
(Show Context)
Citation Context ...he higher-order features of this language that we shall use in the examples in the later sections. A fuller description of the language and of the logical considerations underlying it may be found in =-=[9]-=-. Programs in Prolog are essentially higher-order definite clauses. The following set of clauses that define certain standard list operations serve to illustrate some of the syntactic features of our ... |