Received: from PSUVM.PSU.EDU (psuvm.psu.edu [128.118.56.2]) by locke.ccil.org (8.6.9/8.6.10) with SMTP id WAA13319 for ; Mon, 21 Aug 1995 22:31:22 -0400 Message-Id: <199508220231.WAA13319@locke.ccil.org> Received: from PSUVM.PSU.EDU by PSUVM.PSU.EDU (IBM VM SMTP V2R2) with BSMTP id 4663; Mon, 21 Aug 95 21:58:01 EDT Received: from PSUVM.PSU.EDU (NJE origin LISTSERV@PSUVM) by PSUVM.PSU.EDU (LMail V1.2a/1.8a) with BSMTP id 1773; Mon, 21 Aug 1995 19:35:54 -0400 Date: Tue, 22 Aug 1995 00:07:21 GMT Reply-To: ia@stryx.demon.co.uk Sender: Lojban list From: Iain Alexander Subject: Re: quantifiers X-To: lojban@cuvmb.cc.columbia.edu To: John Cowan Status: OR X-From-Space-Date: Mon Aug 21 22:31:29 1995 X-From-Space-Address: <@PSUVM.PSU.EDU:LOJBAN@CUVMB.BITNET> re fepni pe mi zo'u: doi pycy.n I'm almost certainly misunderstanding _something_ here, so please tell me what it is. As a mathematician (sort of) and computer scientist (more or less), the logical notation I'm familiar with assumes that consecutive quantifiers are nested. (Coordinate quantifiers are not possible in this sort of notation.) Ax Ey x broda y means that for each x there is a y (which is a function of x) such that (x broda y) holds. I had naively assumed that this corresponded to an expression where both quantifiers were in a prenex. If this is indeed the case, it is not at all obvious why 3x 3y x broda y should not also imply that the 'y' quantifier is subordinate to the 'x' one. You didn't appear to like Jorge's suggestion that we use multiple prenexes (prenices?) to denote the nested situation, so I'm not sure a) How you represent nested quantifiers b) How you decide what's nested and what's absolute if you have a mixture of universal, existential and numeric quantifiers in a single prenex. (I'm off to Glasgow for Intersection shortly, so I won't be contributing for a while.) -- Iain Alexander ia@stryx.demon.co.uk I.Alexander@bra0125.wins.icl.co.uk