J. Michael Dunn on Information Based Logics

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.