Abstract
The need to solve structural constraints arises when we investigate computational solutions to the question: “in which logics is a given formula deducible?”This question is posed when one wants to learn the structural permissions for a Categorial Grammar deduction.
This paper is part of a project started at [10], to deal with the question above. Here, we focus on structural constraints, a form of Structurally- Free Theorem Proving, that deal with an unknown transformation X which, when applied to a given set of components P 1...P n, generates a desired structure Q. The constraint is treated in the framework of the combinator calculus as XP 1...P n ↠ Q, where the transformation X is a combinator, the components P iandQ are terms, and ↠reads “reduces to”.
We show that in the usual combinator system not all admissible constraints have a solution; in particular, we show that a structural constraint that represents right-associativity cannot be solved in it nor in any consistent extension of it.To solve this problem, we introduce the notion of a restricted combinator system, which can be consistently extended with complex combinators to represent right-associativity. Finally, we show that solutions for admissible structural constraints always exist and can be efficiently computed in such extension.
Partly supported by the Brazilian Research Council (CNPq), grant PQ 300597/95-5.
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Finger, M. (2001). Computational Solutions for Structural Constraints. In: Moortgat, M. (eds) Logical Aspects of Computational Linguistics. LACL 1998. Lecture Notes in Computer Science(), vol 2014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45738-0_2
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DOI: https://doi.org/10.1007/3-540-45738-0_2
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