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This volume contains several invited papers as well as a selection
of the other contributions. The conference was the first meeting of
the Soviet logicians interested in com- puter science with their
Western counterparts. The papers report new results and techniques
in applications of deductive systems, deductive program synthesis
and analysis, computer experiments in logic related fields, theorem
proving and logic programming. It provides access to intensive work
on computer logic both in the USSR and in Western countries.
Intuitionistic logic is presented here as part of familiar
classical logic which allows mechanical extraction of programs from
proofs. to make the material more accessible, basic techniques are
presented first for propositional logic; Part II contains
extensions to predicate logic. This material provides an
introduction and a safe background for reading research literature
in logic and computer science as well as advanced monographs.
Readers are assumed to be familiar with basic notions of first
order logic. One device for making this book short was inventing
new proofs of several theorems. The presentation is based on
natural deduction. The topics include programming interpretation of
intuitionistic logic by simply typed lambda-calculus (Curry-Howard
isomorphism), negative translation of classical into intuitionistic
logic, normalization of natural deductions, applications to
category theory, Kripke models, algebraic and topological
semantics, proof-search methods, interpolation theorem. The text
developed from materal for several courses taught at Stanford
University in 1992-1999.
Intuitionistic logic is presented here as part of familiar
classical logic which allows mechanical extraction of programs from
proofs. to make the material more accessible, basic techniques are
presented first for propositional logic; Part II contains
extensions to predicate logic. This material provides an
introduction and a safe background for reading research literature
in logic and computer science as well as advanced monographs.
Readers are assumed to be familiar with basic notions of first
order logic. One device for making this book short was inventing
new proofs of several theorems. The presentation is based on
natural deduction. The topics include programming interpretation of
intuitionistic logic by simply typed lambda-calculus (Curry-Howard
isomorphism), negative translation of classical into intuitionistic
logic, normalization of natural deductions, applications to
category theory, Kripke models, algebraic and topological
semantics, proof-search methods, interpolation theorem. The text
developed from materal for several courses taught at Stanford
University in 1992-1999.
Modal Logic can be characterized as the logic of necessity and
possibility, of 'must be' and 'may be'. A Short Introduction to
Modal Logic presents both semantic and syntactic features of the
subject and illustrates them by detailed analyses of the three
best-known modal systems S5, S4 and T. The book concentrates on the
logical aspects of the subject and provides philosophical
motivations to show the point of the formal work. The coverage is
self-contained, including a summary of the necessary aspects of
classical logic which it presupposes. A set of exercises is
included in the final chapter.
Mathematical game theory has been embraced by a variety of
scholars: social scientists, biologists, linguists, and now,
increasingly, logicians. This volume illustrates the recent
advances of game theory in the field. Logicians benefit from things
like game theory's ability to explain informational independence
between connectives; meanwhile, game theorists have even begun to
benefit from logical epistemic analyses of game states. In concert
with such pioneering work, this volume also present surprising
developments in classical fields, including first-order logic and
set theory.
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