Logic and Information

This Element looks at two projects that relate logic and information: the project of using logic to integrate, manipulate and interpret information and the proect of using the notion of information to provide interpretations of logical systems. The Element defines 'information' in a manner that includes misinformation and disinformation and uses this general concept of information to provide an interpretation of various paraconsistent and relevant logics. It also integrates these logics into contemporary theories of informational updating, probability theory and (rather informally) some ideas from the theory of the complexity of proofs. The Element assumes some prior knowledge of modal logic and its possible world semantics, but all the other necessary background is provided. Cover Title Page Imprints Page Logic and Information Contents 1 Logic and Information 1.1 Speed Limits and Firefighters 1.2 What Is Information? Preliminaries 1.3 Information Conditions versus Truth Conditions 1.4 Information States 1.5 Plan of the Element 2 What Is Information? 2.1 Introduction 2.2 Floridi’s Concept of Information 2.3 Information and Data 2.4 Information and Meaning 2.5 Is Information Always Propositional? 2.6 Information and Truth 2.7 So, What Is Information? 2.8 Dretske’s Theory of Information 3 Classical Logic and Its Informational Discontents 3.1 Introduction 3.2 Classical Logic 3.3 Possible Worlds 3.4 Closed Set Semantics 3.5 Partiality and Information 3.6 Situations 3.7 Four-Valued Semantics 3.8 Incompatibility 3.9 Issues Concerning Disjunction 3.10 Implication 3.11 Universal and Local Logics 3.12 Ternary Relation Semantics 3.13 Defeasibility and Implication 3.14 Formal Semantics for Relevant Logic 3.15 Formalising Channel Theory 3.16 The Logic 4 Information, Identity, and Logical Truths 4.1 Introduction 4.2 Frege’s Puzzle 4.3 Content Again 4.4 Extracting Logical Truths 4.5 Upstream and Downstream 5 Updating Information 5.1 Introduction 5.2 Dynamic Logic 5.3 Public Announcement Logic 5.4 Non-Defeasible Updating 5.5 Information, Hard and Soft 5.6 Negative Information 6 Information and Probability 6.1 Introduction 6.2 Probability Functions 6.3 What CBH Is Meant to Measure 6.4 Which Interpretation of Probability? 6.5 Probability as a Guide to Information? 6.6 In Lieu of a Conclusion Bibliography Dedication Published online by Cambridge University Press