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This book celebrates and expands on J. Michael Dunn's work oninformational interpretations of logic. Dunn, in his Ph.D. thesis (1966),introduced a semantics for first-degree entailments utilizing the idea that asentence can provide positive or negative information about a topic, possiblysupplying both or neither. He later published a related interpretation of thelogic R-mingle, which turned out to be one of the first relational semanticsfor a relevance logic. An incompatibility relation between information stateslends itself to a definition of negation and it has figured into Dunn'scomprehensive investigations into representations of various negations. Theinformational view of semantics is also a prominent theme in Dunn's research onother logics, such as quantum logic and linear logic, and led to theencompassing theory of generalized Galois logics (or "gaggles").Dunn's latest work addresses informational interpretations of the ternaryaccessibility relation and the verynature of information.
The book opens withDunn's autobiography, followed by a list of his publications. It then presentsa series of papers written by respected logicians working on different aspectsof information-based logics. The topics covered include the logic R-mingle,which was introduced by Dunn, and its applications in mathematical reasoning aswell as its importance in obtaining results for other relevance logics. Thereare also interpretations of the accessibility relation in the semantics ofrelevance and other non-classical logics using different notions ofinformation. It also presents a collection of papers that develop semantics forvarious logics, including certain modal and many-valued logics.
The publication of thisbook is well timed, since we are living in an "information age." Providingnew technical findings, intellectual history and careful expositions ofintriguing ideas, it appeals to a wide audience of scholars and researchers.
List of contents
Introduction: From Information at Large to Semantics of Logics.-Wedge Sum, Merge and Inconsistency.- LC and its Pretabular Relatives.- EpistemicRelevance and Epistemic Actions.- On Split Negation, Strong Negation,Information, Falsification, and Verification.- Logical Foundations of EvidentialReasoning with Contradictory Information.- Mereocompactness and Duality forMereotopological Spaces.- Syllogistic Logic with Cardinality Comparisons.
About the author
Professor Katalin Bimbó is a logician working in the field of
non-classical logics. Her main research interests and findings are in the areas
of relevance and combinatory logics. She is the author of three books and
numerous journal articles. Professor Bimbó held academic positions in the USA,
New Zealand and Australia before moving to Canada, where she works at the
University of Alberta, in Edmonton.
Summary
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 verynature 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.
