Dynamic Tractable Reasoning: A Modular Approach to Belief Revision (Synthese Library, 420)

Preface
Contents
List of Figures
1 Introduction
	1.1 Apparent Intractability of Belief Changes
	1.2 Computational Theory of Mind
	1.3 Frame Logic
	1.4 TM Belief Revision
	1.5 Modularity in Cognitive Science
	1.6 Modularity in Knowledge Representation
	1.7 Extant Tractable Logics
	1.8 Extant Tractable Belief Revision Schemes
	1.9 Overview
Part I Foundations
	2 Frames
		2.1 Minsky-Frames
			2.1.1 The Abstract Theory
			2.1.2 Examples
			2.1.3 Criticism of the Logistic Approach
		2.2 Classes in Object-Oriented Programming
			2.2.1 The Notion of a Class
			2.2.2 Composition and Inheritance
			2.2.3 Philosophical Logic and OOP
		2.3 Theory-Elements in Structuralism
			2.3.1 Set-Theoretic Structures and Predicates
			2.3.2 Potential and Actual Models
			2.3.3 Intended Applications
			2.3.4 Links and Theory-Nets
	3 Belief Revision
		3.1 Classical Belief Revision Theory
			3.1.1 Beliefs
			3.1.2 Belief Sets
			3.1.3 AGM Postulates for Belief Changes
				3.1.3.1 Expansions
				3.1.3.2 Revisions
				3.1.3.3 Contractions
			3.1.4 Constructive Approaches
		3.2 Belief Base Revision
			3.2.1 Belief Bases
			3.2.2 Belief Bases vs. Belief Sets
			3.2.3 The Direct Mode of Belief Base Revision
		3.3 Some Open Problems in Belief Revision Theory
			3.3.1 Tractability
			3.3.2 The Justificatory Structure
			3.3.3 Epistemic Ordering
	4 Defeasible Reasoning
		4.1 The Rationale
			4.1.1 Common-Sense Reasoning
			4.1.2 Scientific Reasoning
			4.1.3 Consequence vs. Inference Operations
		4.2 Preferred Subtheories
			4.2.1 Basic Ideas
			4.2.2 Inferences from Preferred Subtheories
			4.2.3 A Simple Example
			4.2.4 Belief Revision with Preferred Subtheories
			4.2.5 Reversing the Levi Identity
		4.3 Truth Maintenance
Part II Belief Revision with Frames
	5 Postulates for Structuralism
		5.1 Preliminaries
		5.2 Intended Applications and Theoreticity
		5.3 Intended Applications Liberalised
		5.4 The Postulates
		5.5 Semantics of Theoretical Terms
			5.5.1 Foundations
			5.5.2 Defined Terms
			5.5.3 The Semantics of AE(T)
	6 Structuralist Belief Revision
		6.1 Toward a Default Theory for Structuralism
			6.1.1 Abductive Reasoning in Science
			6.1.2 The Belief Base of a Theory-Net N
		6.2 A Reliabilist Account of Epistemic Ranking
			6.2.1 A Simple Case Study
			6.2.2 The Reliability of Expectations
			6.2.3 The Epistemic Ranking of Theory-Elements
		6.3 The Final Synthesis
	7 Truth Maintenance
		7.1 Computational Complexity and Cognition
			7.1.1 Tractability
			7.1.2 Computation of Revisions
			7.1.3 Cognitive Aspects
		7.2 A Truth Maintenance System for Frames
			7.2.1 Unique Model Extensions
			7.2.2 Logical Foundations of the TMS
			7.2.3 Determining Successful Intended Applications
			7.2.4 Revision by an Intended Application
			7.2.5 Link Satisfaction
			7.2.6 Refinements
				7.2.6.1 Recursive Revisions
				7.2.6.2 Determination Through Links
				7.2.6.3 Retracting Determinations
				7.2.6.4 Updating the Epistemic Ranking
				7.2.6.5 Refining WIDTIO
				7.2.6.6 Prioritising Revise
			7.2.7 The Truth Maintenance Algorithm
		7.3 Tractability
			7.3.1 Operation Tree
			7.3.2 Termination
			7.3.3 Computational Complexity
			7.3.4 Tractability and Modularity
		7.4 Issues of Soundness and Completeness
			7.4.1 The Inference Relation of the TMS
			7.4.2 Admissible T-Extensions
			7.4.3 Division of H(N)
			7.4.4 Subsets of Doubted Applications
			7.4.5 Irrelevant Determinations
			7.4.6 Weak Determinations
			7.4.7 Preliminary Evaluation
		7.5 Approaching Soundness and Completeness
			7.5.1 Composition
			7.5.2 More Defeasible Reasoning
	8 Frame Logic
		8.1 Revising Our Understanding of Links
		8.2 Frame Logic
			8.2.1 Syntax
			8.2.2 Natural Deduction Rules
			8.2.3 Semantics
			8.2.4 Soundness and Completeness
			8.2.5 Tractability
			8.2.6 Composition
		8.3 Resolution Frame Logic
			8.3.1 The Resolution Principle
			8.3.2 Frame Logic with Resolution
			8.3.3 Soundness, Completeness and Tractability
		8.4 Tractable Belief Revision
			8.4.1 Avoiding Irrelevant Determinations
			8.4.2 Weak Determinations Resolved
			8.4.3 TM Belief Revision
			8.4.4 Tractability
			8.4.5 Comparison
		8.5 Truth Maintenance by Resolution
			8.5.1 Resolution-Based Truth Maintenance
			8.5.2 Compositions
			8.5.3 Soundness, Completeness and Tractability
	9 Conclusions
A Proofs
	A.1 Chapter 5
	A.2 Chapter 7
	A.3 Chapter 8
Bibliography
Index of Symbols
Author Index
Subject Index