In this 1992 book, Professor Koslow advances an account of the
basic concepts of logic. A central feature of the theory is that it
does not require the elements of logic to be based on a formal
language. Rather, it uses a general notion of implication as a way
of organizing the formal results of various systems of logic in a
simple, but insightful way. The study has four parts. In the first
two parts the various sources of the general concept of an
implication structure and its forms are illustrated and explained.
Part 3 defines the various logical operations and systematically
explores their properties. A generalized account of extensionality
and dual implication is given, and the extensionality of each of
the operators, as well as the relation of negation and its dual,
are given substantial treatment because of the novel results they
yield. Part 4 considers modal operators and studies their
interaction with logical operators. By obtaining the usual results
without the usual assumptions this new approach allows one to give
a very simple account of modal logic minus the excess baggage of
possible world semantics.
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