The general problem of finding satisfying solutions to constraint-based underspecified representations of quantifier scope is NP-complete. Existing frameworks, including Dominance Graphs, Minimal Recursion Semantics, and Hole Semantics, have struggled to balance expressivity and tractability in order to cover real natural language sentences with efficient algorithms. We address this trade-off with a general principle of coherence, which requires that every variable introduced in the domain of discourse must contribute to the overall semantics of the sentence. We show that every underspecified representation meeting this criterion can be efficiently processed, and that our set of representations subsumes all previously identified tractable sets.

We motivate the integration of programming by example and natural language programming by developing a system for specifying programs for simple text editing operations based on regular expressions. The programs are described with unconstrained natural language instructions, and providing one or more examples of input/output. We show that natural language allows the system to deduce the correct program much more often and much faster than is possible with the input/output example(s) alone, showing that natural language programming and programming by example can be combined in a way that overcomes the ambiguities that both methods suffer from individually, while providing a more natural interface to the user.