From d1761bf08a977c86230b82fbd4b9da0c7b940d78 Mon Sep 17 00:00:00 2001
From: barker
Date: Sat, 18 Sep 2010 16:23:31 -0400
Subject: [PATCH]
---
week2.mdwn | 9 ++++++++-
1 file changed, 8 insertions(+), 1 deletion(-)
diff --git a/week2.mdwn b/week2.mdwn
index 13fd1c89..b23d1a74 100644
--- a/week2.mdwn
+++ b/week2.mdwn
@@ -184,7 +184,14 @@ van Heijenoort (ed) 1967 *From Frege to Goedel,
Cresswell has also developed a variable-free approach of some philosophical and linguistic interest
in two books in the 1990's.
-These systems are Turing complete. In other words: every computation we know how to describe can be represented in a logical system consisting of only a single primitive operation!
+A final linguistic application: Steedman's Combinatory Categorial Grammar, where the "Combinatory" is
+from combinatory logic (see especially his 2000 book, *The Syntactic Process*). Steedman attempts to build
+a syntax/semantics interface using a small number of combinators, including T = \xy.yx, B = \fxy.f(xy),
+and our friend S. Steedman used Smullyan's fanciful bird
+names for the combinators, Thrush, Bluebird, and Starling.
+
+Many of these combinatory logics, in particular, the SKI system,
+are Turing complete. In other words: every computation we know how to describe can be represented in a logical system consisting of only a single primitive operation!
Here's more to read about combinatorial logic.
Surely the most entertaining exposition is Smullyan's [[!wikipedia To_Mock_a_Mockingbird]].
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2.11.0