From nobody@digitalkingdom.org Thu Dec 14 08:47:44 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 14 Dec 2006 08:47:45 -0800 (PST) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.63) (envelope-from ) id 1Gutjv-0000jv-9R for lojban-list-real@lojban.org; Thu, 14 Dec 2006 08:47:23 -0800 Received: from silene.metacarta.com ([65.77.47.18]) by chain.digitalkingdom.org with esmtps (TLS-1.0:DHE_RSA_AES_256_CBC_SHA1:32) (Exim 4.63) (envelope-from ) id 1Gutjn-0000jf-PG for lojban-list@lojban.org; Thu, 14 Dec 2006 08:47:23 -0800 Received: from localhost (silene.metacarta.com [65.77.47.18]) by silene.metacarta.com (Postfix) with ESMTP id 0CD8314C847D for ; Thu, 14 Dec 2006 11:47:14 -0500 (EST) Received: from silene.metacarta.com ([65.77.47.18]) by localhost (silene.metacarta.com [65.77.47.18]) (amavisd-new, port 10024) with ESMTP id 27631-01 for ; Thu, 14 Dec 2006 11:47:09 -0500 (EST) Received: from [65.77.47.178] (cheyenne.metacarta.com [65.77.47.178]) by silene.metacarta.com (Postfix) with ESMTP id 7C62C14C8480 for ; Thu, 14 Dec 2006 11:32:31 -0500 (EST) Message-ID: <45817C9F.8000309@ropine.com> Date: Thu, 14 Dec 2006 11:32:31 -0500 From: Seth Gordon User-Agent: Debian Thunderbird 1.0.2 (X11/20060926) X-Accept-Language: en-us, en MIME-Version: 1.0 To: lojban-list@lojban.org Subject: [lojban] Re: Using continuations to model quantifiers, focus, and coordination References: <45816F09.4060602@ropine.com> <975a94850612140811g34d5f43ay278323c463f2538d@mail.gmail.com> In-Reply-To: <975a94850612140811g34d5f43ay278323c463f2538d@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Virus-Scanned: by amavisd-new-20030616-p10 (Debian) at metacarta.com X-Spam-Score: -2.6 (--) X-archive-position: 13362 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: sethg@ropine.com Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list Joel Shellman wrote: >> There is a theory of grammar that maps sentences onto logical functions, >> but this theory has trouble handling quantifiers like "everyone", >> "someone", and "only". If I want to parse "Matt spoke", I can treat >> "Matt" as an individual and treat "spoke" as a function that maps an >> individual onto a truth value (given X, did X speak?). But if I use the >> same system to parse "Everyone spoke", "everyone" is not an individual >> but a function in itself (given an individual X and an action Y, did X >> do Y?). Furthermore, if we turn to the sentence "Matt spoke to >> everyone", it seems like we need to interpret "everyone" as a function >> of another type. > > > I'm not sure I follow. To me, everyone is the set of all people (or > possibly less or different depending on context--"everyone in the > room" is the set of all people present in that room). > > Applying functions on sets shouldn't be a problem, is it? I suspect that rephrasing all of this in terms of set theory would run into the problem that "set of A" is not the same logical type as "A". So you can't translate "Everyone on this list loves Lojban" to "the set of everyone in this list loves Lojban"; you have to translate it to "for all X such that X is a member of the set of everyone in this list, X loves Lojban". Once you've done that transformation, a Prolog-like logic engine can reduce "does Matt love Lojban?" to "is Matt is on this list?". (Note how the word "everyone" is embedded within the sentence "Everyone on this list loves Lojban" and yet its effect on the logical rephrasing encompasses the whole sentence; consider, too, how one would rephrase "Matt loves everyone's native language". This inside-out effect is the sort of thing that continuations are very good at formalizing.) To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.