J. Michael Dunn on Information Based Logics

Description

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. Front Matter....Pages i-xliii Introduction: From Information at Large to Semantics of Logics....Pages 1-14 \(\mathbf {RM}\) and its Nice Properties....Pages 15-43 Wedge Sum, Merge and Inconsistency....Pages 45-51 Single Axioms and Axiom-Pairs for the Implicational Fragments of \(\mathbf {R}\) , R-Mingle, and Some Related Systems....Pages 53-80 LC and Its Pretabular Relatives....Pages 81-91 The Story of \(\gamma \) ....Pages 93-105 Manipulating Sources of Information: Towards an Interpretation of Linear Logic and Strong Relevance Logic....Pages 107-131 Epistemic Relevance and Epistemic Actions....Pages 133-146 Comparing Contents with Information....Pages 147-159 On Split Negation, Strong Negation, Information, Falsification, and Verification....Pages 161-189 Truth, Falsehood, Information and Beyond: The American Plan Generalized....Pages 191-212 Logical Foundations of Evidential Reasoning with Contradictory Information....Pages 213-246 Probabilistic Interpretations of Predicates....Pages 247-278 Reasoning with Incomplete Information in Generalized Galois Logics Without Distribution: The Case of Negation and Modal Operators....Pages 279-312 Mereocompactness and Duality for Mereotopological Spaces....Pages 313-330 Distributed Modal Logic....Pages 331-362 Tracking Information....Pages 363-389 Syllogistic Logic with Cardinality Comparisons....Pages 391-415 A “Reply” to My “Critics”....Pages 417-434 Back Matter....Pages 435-436