A Brief History of Natural Logic
Johan van Benthem

Abstract:
'Natural logic' is the idea that much human inference
can be based on natural language surface form, which
(hopefully) reflects fast human computational-cognitive 
mechanisms. This paper was written at the invitation of 
the computational linguists at Stanford, who are using 
light inference mechanisms in current avant-garde text 
processing. We trace the sources of the idea to pre-
Fregean traditional logic, and explain the systematic 
categorial 'monotonicity calculus' allowing inference 
a 'free ride' on syntax, first proposed in the 1980s 
in the setting of generalized quantifier theory, as 
well as subsequent developments - all the way up to 
current cognitive science. Calculi of natural logic 
belong to the most frequently rediscovered ideas in 
logic: from philosophy in Greek and Chinese Antiquity 
to modern computer science and neuroscience. The paper 
will appear in the "Proceedings of the Kolkata Logic 
Conference 2007", held in the memory of K. Matilal,
edited by Benedikt Loewe, Sujata Ghosh, et al.