This book celebrates and expands on J. Michael Dunns 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 Dunns research onother logics, such as quantum logic and linear logic, and led to theencompassing theory of generalized Galois logics (or "gaggles").Dunns latest work addresses informational interpretations of the ternaryaccessibility relation and the verynature of information.
The book opens withDunns 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.
Professor Katalin Bimbó is a logician working in the field ofnon-classical logics. Her main research interests and findings are in the areasof relevance and combinatory logics. She is the author of three books andnumerous journal articles. Professor Bimbó held academic positions in the USA,New Zealand and Australia before moving to Canada, where she works at theUniversity of Alberta, in Edmonton.
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, Falsication, and Verication.- Logical Foundations of EvidentialReasoning with Contradictory Information.- Mereocompactness and Duality forMereotopological Spaces.- Syllogistic Logic with Cardinality Comparisons.
