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204:; phenotype corresponds closely to the actual language, as in the previous graphic. Genotype is a more universal structure for the meaning. For the sake of clearer focus on genotype issues, tree branch order can be rendered so that functions are to the left of their arguments. A more genotypical parse tree looks like this:
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AUG has just two primitive types: T for terms, S for "sentences" (though AUG apparently allows for sentence fragments being of type S.) There is one non-primitive type, that returns a function: Oxy. O reduces x and y to another type, xy, that combines the types of x and y, xy. Words can be functions
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The intransitive "lives" is typed OTS: the subject is a T, but an S -- a sentence phrase -- must be the resulting type. Why does "in" have type OTOOTSOTS? "In" as a three-place function requires a location ("Boston"; type T), something happening ("lives"; type OTS), and in this example, a subject,
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Note that making O a prefix operator obviates the need for parentheses (as in more conventional mathematical orthography), and makes for a more compact presentation on the page.
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of this type. The type of a word like "my" (thing) is OTT: it takes something of type T and yields something of type T. "My friend" has a structure like this:
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The word "living" gets reduced to the more specific "living in Boston". AUG distinguishes between
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AUG allows both forward and backward application of O. Here is the rule for backward application:
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103:{\displaystyle {\dfrac {\text{''my'' :: OTT ''friend'' :: T}}{\text{''my friend'' :: T}}}}
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COLING '94: Proceedings of the 15th conference on
Computational linguistics
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275:(1st ed.). Bloomington and Indianapolis: Indiana University Press.
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186:{\displaystyle {\dfrac {\text{q :: x p :: Oxy}}{\text{q p :: y}}}}
138:{\displaystyle {\dfrac {\text{p :: Oxy q :: x}}{\text{p q :: y}}}}
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theory that views the formation of phrase structure by analogy to
406:, Workshops in Computer Science Series.(IFIP), Springer-Verlag,
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are the ideas of functional superposition and stratified types.
349:"Long-Distance Dependencies and Applicative Universal Grammar"
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Proceedings of the
Glasgow Workshop on Functional Programming
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Applicative
Grammar as a Semantic Theory of Natural Language
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Here is how "my friend lives in Boston" reduces in AUG.
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70:, which describes an implementation of AUG parsing in
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463:"An Introduction to Applicative Universal Grammar"
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113:Rules can transform p of type Oxy to q of type x:
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31:processes in particular languages. This is a
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43:. Among the innovations in this approach to
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393:"Using Types to Parse Natural Language"
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41:applicative programming language
92:''my'' :: OTT ''friend'' :: T
446:. Edinburgh University Press.
235:Combinatory categorial grammar
1:
558:Applicative computing systems
273:A Semiotic Theory of Language
225:Applicative computing systems
17:Applicative universal grammar
501:. You can help Knowledge by
45:natural language processing
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301:"Functional Superposition"
27:intended for studying the
23:, is a universal semantic
320:Brigham Young University
461:Sypniewski, Bernard P.
548:Philosophy of language
497:-related article is a
413:10.14236/ewic/FP1995.0
297:Bernard P., Sypniewski
240:Functional programming
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55:In the paper entitled
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328:10.3115/991250.991285
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37:function application
442:(January 1, 1977).
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269:Shaumyan, Sebastian
345:Segond, Frédérique
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362:: 853–858,
322:: 279–287,
542:Categories
256:References
64:Paul Hudak
33:linguistic
472:April 29,
299:(2009) ,
198:phenotype
391:(1995),
347:(1994),
271:(1987).
219:See also
178:q p :: y
130:p q :: y
29:semantic
495:grammar
402:(ed.),
72:Haskell
51:Example
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39:in an
493:This
398:, in
396:(PDF)
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19:, or
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474:2021
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408:doi
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21:AUG
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
