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This is the first book-length treatment of hybrid logic and its
proof-theory. Hybrid logic is an extension of ordinary modal logic
which allows explicit reference to individual points in a model
(where the points represent times, possible worlds, states in a
computer, or something else). This is useful for many applications,
for example when reasoning about time one often wants to formulate
a series of statements about what happens at specific times. There
is little consensus about proof-theory for ordinary modal logic.
Many modal-logical proof systems lack important properties and the
relationships between proof systems for different modal logics are
often unclear. In the present book we demonstrate that
hybrid-logical proof-theory remedies these deficiencies by giving a
spectrum of well-behaved proof systems (natural deduction, Gentzen,
tableau, and axiom systems) for a spectrum of different hybrid
logics (propositional, first-order, intensional first-order, and
intuitionistic).
This book is the first book-length treatment of hybrid logic and
its proof-theory. Hybrid logic is an extension of ordinary modal
logic which allows explicit reference to individual points in a
model. The extra expressive power is useful for many applications,
for example, when reasoning about time one often wants to formulate
a series of statements about what happens at specific times. There
is little consensus about proof-theory for ordinary modal logic.
Many modal-logical proof systems lack important properties and the
relationships between proof systems for different modal logics are
often unclear. The present book demonstrates that hybrid-logical
proof-theory remedies this lack of uniformity in ordinary
modal-logical proof systems. It considers a spectrum of different
versions of hybrid logic (propositional, first-order, international
first-order, and intuitionist) and of different types of
proof-systems for hybrid-logic (natural deduction, Gentzen,
tableaux, and axiom systems). All these systems can be motivated
independently, but the fact that the systems can be given in a
uniform way shows that hybrid logic and hybrid-logical proof theory
is a natural enterprise.
Modal logic is a subject with ancient roots in the western logical
tradition. Up until the last few generations, it was pursued mainly
as a branch of philosophy. But in recent years, the subject has
taken new directions with connections to topics in computer science
and mathematics. This volume is the proceedings of the conference
of record in its fi eld, Advances in Modal Logic. Its contributions
are state-of-the-art papers. The topics include decidability and
complexity results for specifi c modal logics, proof theory of
modal logic, logics for reasoning about time and space, provability
logic, dynamic epistemic logic, and the logic of evidence.
This is a revised and expanded edition of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior (1914-1969) was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the Polish logic which made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book.
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