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Higher-order linear logic programming of categorial deductionby: Glyn Morrill
In Proceedings of the seventh conference on European chapter of the Association for Computational Linguistics (1995), pp. 133-140.
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Notes for this articleThis paper very neatly anticipates Frank's and my translation of ordered logic into linear logic, but does so in a rather obfuscated way that doesn't lead to a general treatment of linear logic that we need for our framework; furthermore, it is very "horn-oriented" and does not deal with existential creation. However, the stuff me and Frank have positied is possible should almost certainly be seen as a straightforward generalization of this to a higher-powered version of ordered logic.
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AbstractWe show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing problem of Lambek categorial grammar applicable to a variety of its extensions.
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