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Paper available: Linear Logic complements Classical Logic
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The paper described below is available by FTP or the web as follows.
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Linear Logic complements Classical Logic
V.R. Pratt
To appear in preliminary proceedings of Linear Logic '96, Tokyo
Classical logic enforces the separation of individuals and predicates,
linear logic draws them together via interaction; these are not
right-or-wrong alternatives but dual or complementary logics. Linear
logic is an incomplete realization of this duality. While its
completion is not essential for the development and maintenance of
logic, it is crucial for its application. We outline the
``four-square'' program for completing the connection, whose corners
are set, function, number, and arithmetic, and define ordinal Set, a
bicomplete *equational* topos, meaning its canonical isomorphisms are
identities, including associativity of product.
This directory also contains 44 other papers on related topics. For a
list of abstracts, see the file ABSTRACTS in this directory, URL:
http://boole.stanford.edu/pub/ABSTRACTS
Vaughan Pratt