FOM: Book recommendation

Joe Shipman shipman at
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 

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 

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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