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This book celebrates and expands on J. Michael Dunn’s work on
informational interpretations of logic. Dunn, in his Ph.D. thesis (1966),
introduced a semantics for first-degree entailments utilizing the idea that a
sentence can provide positive or negative information about a topic, possibly
supplying both or neither. He later published a related interpretation of the
logic R-mingle, which turned out to be one of the first relational semantics
for a relevance logic. An incompatibility relation between information states
lends itself to a definition of negation and it has figured into Dunn's
comprehensive investigations into representations of various negations. The
informational view of semantics is also a prominent theme in Dunn’s research on
other logics, such as quantum logic and linear logic, and led to the
encompassing theory of generalized Galois logics (or "gaggles").
Dunn’s latest work addresses informational interpretations of the ternary
accessibility relation and the very nature of information.
The book opens with
Dunn’s autobiography, followed by a list of his publications. It then presents
a series of papers written by respected logicians working on different aspects
of information-based logics. The topics covered include the logic R-mingle,
which was introduced by Dunn, and its applications in mathematical reasoning as
well as its importance in obtaining results for other relevance logics. There
are also interpretations of the accessibility relation in the semantics of
relevance and other non-classical logics using different notions of
information. It also presents a collection of papers that develop semantics for
various logics, including certain modal and many-valued logics.
The publication of this
book is well timed, since we are living in an "information age.” Providing
new technical findings, intellectual history and careful expositions of
intriguing ideas, it appeals to a wide audience of scholars and researchers.