Carpenter (carp@lcl.cmu.edu)
Mon, 8 Aug 94 16:39:03 edt
I just thought I'd add my two bits to the fray concerning coordination. I believe there are two very promising approaches that should meet Carl Pollard's objectives of a unified account of gapping, ellipsis, constituent coordination, right-node raising, coordination of 'unlike categories' and so on. The first piece of the puzzle is the theory of ellipsis developed by Dalrymple, Pereira and Shieber ("Ellipsis and Higher-Order Unification", Linguistics and Philosophy 14, 399--452, 1991). The basic idea behind their approach is that by setting up an equation among the parallel elements in an elliptical construct, the material that was ellided can be determined retroactively. For instance, in John ran and Fred did, too we get the equation: P(john) = run(john) ==> P = run because John is the parallel element to Fred. Then we substitute Fred in for John, to solve for the second conjunct: P(fred) = run(fred) The beauty of this theory is that it can be extended to all sorts of cases, with quantifier scope ambiguities, negation, tense and all kinds of parallelism. Their theory can naturally be extended to gapping, with the same notion of parallelism. This has been done by one of my students, Akira Ushioda, and applied to Japanese, which presents an even greater difficulty for reconstructive theories. Ushioda extended Dalrymple et al. to gapping and ordinary coordination, including right-node raising, etc. For instance, consider: John gave Bill beans and Fred tomatos. This would produce the equation: P(bill,beans) = give(john,bill,beans) [P(x,y) = give(john,x,y)] The second conjunct is then reconstructed to P(fred,tomatos) = give(john,fred,tomatos) I now believe that this approach subsumes the standard approach in categorial grammars of the Lambek variety, which allow arbitrary amounts of type-raising to allow all sorts of coordination, and can be extended to gapping, as shown by Glyn Morrill in his forthcoming book, "Type Logical Grammmar: A categorial theory of signs", Kluwer (in press -- should be out any day). While I don't think Morrill's approach to gapping is a necessary addition to the Dalrymple et al. approach, I do believe another issue discussed in Morrill's book is critical, and that's the proper treatment of the logic of categories. In theories like HPSG, we have a sound representation of conjunction, but not disjunction. Morrill provides a logic based on the ordinary logical introduction and elimination rules for the logical connectives (subcat is like implication). The main analysis is that of copula complement coordination (usually referred to as "unlike categories", but as with most of CG, they're turned into "like categories"). For instance, 'is' would get a lexical entry with the following subcat frame (translating into HPSG notation): s[np, (np OR adj OR vp OR pp)] The real heart of this result is that the ORs in the categories can be tied up to if-then rules in the lambda calculus (the standard interpretation of disjunctive types -- by disjoint sums, according to the Curry-Howard morphism). So the semantics can be conditioned to depend not only on the argument's semantics, but also on its type, so that a different result can be achieved depending on which complement of the copula is chosen, because they're of different types. This is a form of limited polymorphism. But the punchline is that now we can have derivations like the following (simplified a bit): is a hero and in the house ----------------- ----- ---------- s[np, (np OR pp)] np pp ---- ---------- (np OR pp) (np OR pp) -------------------------- (np OR pp) ------------------------------------- s[np] The key is the introduction scheme for disjunction, which allows us to conclude that if 'a hero' is of category np, then it is of the more general category (np OR pp). I won't include the semantic details, as they're a bit complicated if you're not familliar with disjoint sums. Further, we get the following kind of equivalences: s[np, (np OR pp)] == s[np,np] AND s[np,pp] This is analogous to the following logical equivalence: (np OR pp) -> np -> s === (np -> np -> s) AND (pp -> np -> s) Thus the logic allows the ordinary copula complements to be derived one at a time. Most lexicons don't allow conjunction or disjunction inside of the categories, but Morrill shows that its logic is the natural one. I should also point out that this approach significantly improves on the approach suggested by Karttunen, which involves generalization (sometimes called anti-unification). It is well known that generalization loses information and is not sound for natural langauge coordination. Now, the real question is whether this will fit in with HPSG. I don't know the answer. Fernando Pereira assures me that their theory can be applied to theories like LFG and doesn't depend on higher-order unification, but merely on being able to undo semantic operations in a uniform way. I don't think there'd be any problem in rendering Morrill's logic of categories into HPSG, though it would require a lot of work on the interpretation of categories. PS Akira Ushioda's paper should be available soon -- his e-mail is: aushioda@lcl.cmu.edu - Bob Carpenter Computational Linguistics Program, Philosophy Department Carnegie Mellon University, Pittsburgh, PA 15213 Net: carp@lcl.cmu.edu Phone: (412) 268-8043 Fax: (412) 268-1440
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