FOM: Book recommendation
Joe Shipman
shipman at savera.com
Fri Aug 4 00:22:19 EDT 2000
Please take a look at "Extensions of First Order
Logic", by Maria Manzano (Cambridge Tracts in
Theoretical Computer Science 19, Cambridge
University Press 1996, ISBN 0-521-35435-8, xxii+388
pages). It sheds a good deal of light on the recent
FOM discussions of second-order logic, Henkin
semantics, etc. (Henkin was her advisor). There is a
very impressive amount of detail about various logics
and their relations.
I quote from the preface:
>>
This book considers various extensions of first order
logic, giving detailed and elaborate treatment to many
useful logical systems: second order logic (SOL), type
theory (RTT, ETT anf FTT), modal logic (PML and FOML),
dynamic logic (PDL) and many-sorted logic (MSL). A
substantial dose of logical perspective is also
provided.
The second objective of this book is to pursue the
thesis that most reasonable logical systems can be
naturally translated into many-sorted first order
logic. The thesis is maintained throughout the book,
but only appears openly and explicitly int the last
chapter. There, all the logic systems treated in the
book are put in direct correspondence with many-sorted
logic because this logic offers a unifying framework in
which to place other logics. In itself, many-sorted
logic is a natural logic for formalizing statements in
a great variety of disciplines and it also has an
efficient proof theory with a complete deductive
calculus.
Currently, the proliferation of logics used in
philosophy, computer science, artificial intelligence,
mathematics, and linguistics make a working reduction
of this variety an urgent issue. The aim is two-fold:
-- To be able to use only one deductive calculus and a
unique theorem prover for all logics --i.e. an MSL
theorem prover;
-- To avoid the proofs of the metaproperties of the
different existing logics by borrowing them from many-
sorted logic.
<<
-- Joe Shipman
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