From nobody@digitalkingdom.org Thu Jul 13 14:11:48 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 13 Jul 2006 14:11:49 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G18T2-0002Oh-Jm for lojban-list-real@lojban.org; Thu, 13 Jul 2006 14:11:28 -0700 Received: from web81315.mail.mud.yahoo.com ([68.142.199.41]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G18T0-0002OX-Ix for lojban-list@lojban.org; Thu, 13 Jul 2006 14:11:28 -0700 Received: (qmail 79800 invoked by uid 60001); 13 Jul 2006 21:11:25 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=sbcglobal.net; h=Message-ID:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding; b=v0i2EOkU4xS6XXN7fT/5nuAmlymFjdjyW5zMD5eSUeJPH67q40b66V83y6b6mBjI3T6k0n6TTf2NYTRjwKDZHW8c32YvolZqKqB6UDFVFJxoWRfqdssVVlPl38im5HNNKjt4EgUgZc0msLx9o3HUykRnhzzx6pKZzbYKxN2MHHk= ; Message-ID: <20060713211125.79798.qmail@web81315.mail.mud.yahoo.com> Received: from [70.230.188.85] by web81315.mail.mud.yahoo.com via HTTP; Thu, 13 Jul 2006 14:11:25 PDT Date: Thu, 13 Jul 2006 14:11:25 -0700 (PDT) From: John E Clifford Subject: [lojban] Re: A (rather long) discussion of {all} To: lojban-list@lojban.org In-Reply-To: <925d17560607130536u49e124eav6370db221f510467@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.6 (/) X-archive-position: 12191 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list I send this along for corrections and questions before using it (in its revised form) to answer Maxim's questions. Singular v. Plural Semantics Language: Variables: Names: Predicates: Relation: A Sentential connectives: ~, & (others by usual definitions) Quantifiers: E Descriptor: t Terms: a variable is a term, a name is a term, if F is a formula containing free variable x, then txF is a term. Formula: A predicate followed by a term is a formula, A followed by two terms is a formula, a formula preceded by ~ is a formula, two formulas preceded by & is a formula, a formula preceded by a variable preceded by E is a formula A formula contains a free variable x just in case there is an occurrence of x in that formula which is not in any subformula which begins Ex nor in a term which begins tx A sentence is a formula which contains no free variables. A singularist model: Domain D: a non-empty set Masses M: Power D – 0. the set of all non-empty subsets of D Concepts: Interpretation: a function, I that assigns to: Each concept an object from M Each name a concept Each predicate a function from concepts into {0, 1} I(A) is the function from pairs of concepts such that I(A)(c1,c2) = 1 iff I(c1) is included in I(c2) A is an assignment iff A is a function from variables to concepts A(c/x) is an assignment just like A except that it assigns the concept c to variable x instead of A(x). If a is a term, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, R(a) is a concept c such that F is true for A(c/x), if a = txF i is an individual just in case i is in M and is a subset of each of its subsets (is identical with each of its subsets, has only one member). Where P is a predicate and a a term, Pa is d-true for I and A iff for every individual i included in R(a) and for every concept c s.t. I(c) = i, I(P)(c) = 1 Where P is a predicate and a a term, Pa is c-true for I and A iff I(P)(R(a)) = 1 A Pluralist model Domain: Some things Concepts C is a relation between concepts and items in D, such that for every d in D, there is at least once c such that c is related by C only to d (C/d) And interpretation I is a function which assigns To each name a concept To each predicate a function from concepts into {0,1} To A the function from pairs of concepts into {0,1} such that I(A)(R(a)R(b)) = 1 iff for every thing d such that R(a)Cd holds, R(b)Cd holds An assignment A is a function from variable to concepts A(c/x) is an assignment just like A except for assigning c to x in place of A(x). For term a, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, is a concept c such that F is true for I and A (c/x) if a = txF Pa is d-true for I and A iff for every d such that R(a)Cd, I(P)(C/d) = 1 Pa is c-true for I and A iff I(P)(R(a)) = 1 In either case, A formula F is true for I and A If it is Pa, for some predicate P and some term a and either Pa is d-true for I and A or Pa is c-true for I and A If it is Aab and I(A)(R(a) R(b)) =1 If it is ~S for some formula S and S is not true for I and A It is &GH for some formulae G and H and both G and H are true for I and A It is ExG for some variable x and some formula G and for some concept c, G is true for I and A(c/x) Otherwise not. 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.