{"id":2438,"date":"2025-10-06T12:26:58","date_gmt":"2025-10-06T16:26:58","guid":{"rendered":"https:\/\/www.wellformedness.com\/blog\/?p=2438"},"modified":"2025-11-03T13:56:41","modified_gmt":"2025-11-03T18:56:41","slug":"linking-constraint-exhaustification","status":"publish","type":"post","link":"https:\/\/www.wellformedness.com\/blog\/linking-constraint-exhaustification\/","title":{"rendered":"The linking constraint and exhaustification"},"content":{"rendered":"<p>Hayes (1986) proposes the <em>linking constraint<\/em>, a convention for the interpretation of autosegmental rules. As stated, it holds that association lines should be &#8220;interpreted as exhaustive&#8221;. In the context of a rule, this means that the target and triggers are not permitted to have additional linkages not mentioned in the rule.<\/p>\n<p>Later in the paper, Hayes makes it clear that this is to be interpreted with respect to whatever tiers are mentioned. For example, imagine a rule that manipulates the melodic\/featural tier but is conditioned in part by the CV tier\u2014Hayes adopts CV theory, but the &#8220;constraint&#8221; is just as applicable to approaches which use an X and\/or moraic tier\u2014then the rule does not apply to any susbstring of the melody whose melodies contain associations to the CV tier not mentioned. Similarly, imagine a rule that targets elements on the CV tier but is conditioned in part by the melody: such a rule would not apply to any substring of the CV tier with associations to the melody not explicitly stated in the rule.<\/p>\n<p>I would like to claim that this is all too informal. It should be possible to state the substring that matches the rule using something like first-order logic (FOL), and similarly to translate the change into a logical statement. However, it&#8217;s not immediately clear how to write the procedure that translates autosegmental diagrams into the appropriate FOL sentences. (I put aside the encoding of the change: I think this will be comparatively easy.) Autosegmental diagrams itself are essentially an fragment of undirected graph, and translating these into FOL statements is straightforward enough: the description of the graph is defined by the logical conjunction of:<\/p>\n<ul>\n<li>one-place predicates stating what type each element is (i.e., what tier its on),<\/li>\n<li>two-place immediate-precedence predicates (when the rule refers to\u00a0 multiple elements on a given tier),<\/li>\n<li>two-place (unordered) predicates indicating the association lines between tiers.<\/li>\n<\/ul>\n<p>To enforce the linking constraint, one needs to add additional predicates to this conjunction that rule out associations not mentioned. Conceptually, I think of this as an <em>exhaustification function <\/em>(with apologies for the abuse of terminology) which takes the graph description above and returns the predicates needed to rule out forbidden associations in the relevant subgraphs. While I think I know what these exhaustifying predicates need to be for toy examples, I don&#8217;t yet know what the general algorithm is.<\/p>\n<p>I am also somewhat concerned whether phonologists are (were?) applying the linking convention in a vibes-based fashion depending on the example in question, in which case no algorithm could properly describe analytical practices. Finally, I am interested in the feasibility of the opposite approach\u2014a road not taken, as far as I know, in autosegmental theory\u2014 whereby undesired associations are ruled out simply by making the rule more explicit.<\/p>\n<p>Does anyone know of any relevant work on this topic? Surely I am not the first person to be bothered by this.<\/p>\n<h1>References<\/h1>\n<p>Hayes, B. 1986. Inalterability in CV phonology.\u00a0<em>Language <\/em>62: 321-351.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hayes (1986) proposes the linking constraint, a convention for the interpretation of autosegmental rules. As stated, it holds that association lines should be &#8220;interpreted as exhaustive&#8221;. In the context of a rule, this means that the target and triggers are not permitted to have additional linkages not mentioned in the rule. Later in the paper, &hellip; <a href=\"https:\/\/www.wellformedness.com\/blog\/linking-constraint-exhaustification\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;The linking constraint and exhaustification&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","footnotes":""},"categories":[4,6],"tags":[],"class_list":["post-2438","post","type-post","status-publish","format-standard","hentry","category-language","category-phonology"],"_links":{"self":[{"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/posts\/2438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/comments?post=2438"}],"version-history":[{"count":5,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/posts\/2438\/revisions"}],"predecessor-version":[{"id":2457,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/posts\/2438\/revisions\/2457"}],"wp:attachment":[{"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/media?parent=2438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/categories?post=2438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wellformedness.com\/blog\/wp-json\/wp\/v2\/tags?post=2438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}