tag:blogger.com,1999:blog-5275657281509261156.post6119012376095973002..comments2024-03-28T04:04:55.806-07:00Comments on Faculty of Language: Aspects at 50Norberthttp://www.blogger.com/profile/15701059232144474269noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5275657281509261156.post-51639779282181261472015-06-27T16:48:49.136-07:002015-06-27T16:48:49.136-07:00@INCOLLECTION{PetersRitchie73a,
author = {Peters...@INCOLLECTION{PetersRitchie73a,<br /> author = {Peters, Stanley and Ritchie, Robert W.},<br /> title = {Non-Filtering and Local-Filtering Transformational Grammars},<br /> year = {1973},<br /> editor = {Hintikka, Jaakko and Moravcsik, J.M.E. and Suppes, Patrick},<br /> booktitle = {Approaches to Natural Language},<br /> publisher = {Reidel},<br /> address = {Dordrecht},<br /> pages = {180--194}<br />}<br /><br />Let me flesh out the technical side a bit. P&R show that a transformational grammar restricted to context-free D-structures and local-filtering transformations is rather peculiar with respect to weak generative capacity. The claims I made above are established as follows:<br /><br />1) The fact that every context-free language can be generated is an immediate consequence of the context-freeness of D-structures.<br />2) These restricted transformational grammars cannot generate the language a^(2^(2^n)), which is context-sensitive.<br />3) P&R show that every recursively enumerable language is the intersection of some transformational language with a regular language. But since the next weaker class --- the class of recursive languages --- is closed under intersection with regular languages, the previous result can hold only if transformational grammars generates some non-recursive (and thus recursively enumerable) languages.<br /><br />One minor correction to what I said in point 2 above: the paper does not show that some properly context-sensitive languages are generated by this formalism. It is in principle possible that expressivity jumps immediately from context-free all the way up to a specific subset of the recursively enumerable languages. That said, I am pretty sure that context-sensitive languages like a^n b^n c^n or a^(2^n) can be generated by the formalism, though I haven't worked out specific transformational grammars for these languages.Anonymoushttps://www.blogger.com/profile/07629445838597321588noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-18071964198539878852015-06-27T10:26:46.231-07:002015-06-27T10:26:46.231-07:00@Thomas Graf What's the reference for the foll...@Thomas Graf What's the reference for the follow-up P&R paper?Utpalhttps://www.blogger.com/profile/18166651069703369369noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-88762358959127486032015-06-26T11:13:57.378-07:002015-06-26T11:13:57.378-07:00Interesting that you liken Minimalism to Syntactic...Interesting that you liken Minimalism to Syntactic Structures rather than Aspects. One could just as well analyze Minimalism as a return to Aspects: Deep Structure is furnished by derivation trees, which can be described in terms of context-free phrase structure grammars, and derivation trees are mapped to phrase structure trees that are only linearly bigger (unless you have overt copying). There is also a difference between Merge and Move in that the mapping brings about major structural changes for the former but not the latter.<br /><br />I like this perspective because it highlights that we have made a lot of progress in characterizing this mapping. Peters & Ritchie showed that Aspects didn't have a good handle of that, that's why you got the Turing equivalence with even very harsh restrictions on D-Structure. They also pointed out in a follow-up paper (which seems to have been ignored at the time of publishing) that bounding the mapping with respect to the size of D-Structure lowers expressivity quite a bit. What you get is a non-standard class that generates<br /><br />1) all context-free languages,<br />2) some but not all context-sensitive languages,<br />3) some (properly) recursively enumerable languages.<br /><br />In hindsight, we can recognize this as a first rough approximation of the mildly context-sensitive language. So Aspects was on the right track, but the mapping was still too powerful --- and also too complicated, which is why the Peters and Ritchie proofs are pretty convoluted. Unifying all transformations in terms of a few strongly restricted movement operations (and doing away with deletion) has really cleared things up.<br /><br />Just to be clear, I'm not saying that your characterization is less adequate. Rather, this is a nice demonstration that one and the same piece of technical machinery can be conceptualized in various ways to highlight different aspects.Anonymoushttps://www.blogger.com/profile/07629445838597321588noreply@blogger.com