From b430b8ab71a7bfe996a8b34b570b4469afd73ca5 Mon Sep 17 00:00:00 2001 From: Chris Date: Tue, 7 Apr 2015 22:21:44 -0400 Subject: [PATCH] edits --- topics/_week10_gsv.mdwn | 56 +++++++++++++++++++++++++++++++++++++++++++------ 1 file changed, 50 insertions(+), 6 deletions(-) diff --git a/topics/_week10_gsv.mdwn b/topics/_week10_gsv.mdwn index 3fd046c9..e971fe93 100644 --- a/topics/_week10_gsv.mdwn +++ b/topics/_week10_gsv.mdwn @@ -150,10 +150,54 @@ in terms of negation and the other connectives. Exercise: assume that there are two entities in the domain of discourse, Alice and Bob. Assume that Alice is a woman, and Bob is a -man. Show the following computations: +man. Show the following computations, where `i = (w,n,r,g)`: + + 1. {i}[âx.person(x)] + + = {(w,n+1,r[x->n],g[n->a]),(w,n+1,r[x->n],g[n->b])}[person(x)] + = {(w,n+1,r[x->n],g[n->a]),(w,n+1,r[x->n],g[n->b])} + + 2. {i}[âx.man(x)] + + = {(w,n+1,r[x->n],g[n->a]),(w,n+1,r[x->n],g[n->b])}[person(x)] + = {(w,n+1,r[x->n],g[n->b])} + + + 3. {i}[âxây.person(x) and person(y)] + + = {(w,n+1,r[x->n],g[n->a]),(w,n+1,r[x->n],g[n->b])}[ây.person(x) and person(y)] + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + }[person(x) and person(y)] + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + } + + 4. {i}[âxây.x=x] + + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + }[âxây.x=x] + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + } + + 5. {i}[âxây.x=y] + + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + }[âxây.x=y] + = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]), + (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b]) + } - 1. {}[âx.person(x)] - 2. {}[âx.man(x)] - 3. {}[âxây.person(x) and person(y)] - 4. {}[âxây.x=x] - 5. {}[âxây.x=y] -- 2.11.0