Abstract
We show how to compute readings of ambiguous natural language sentences that are minimal in some way. Formally, we consider the problem of computing, out of a set C of trees and a rewrite system R, those trees in C that cannot be rewritten into a tree in C. We solve the problem for sets of trees that are described by semantic representations typically used in computational linguistics, and a certain class of rewrite systems that we use to approximate entailment, and show how to compute the irreducible trees efficiently by intersecting tree automata. Our algorithm solves the problem of computing weakest readings that has been open for 25 years in computational linguistics.
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