| Description |
1 online resource (241 pages) |
| Series |
Synthese library ; v. 420 |
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Synthese library ; v. 420.
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| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. This book conducts a sustained and detailed examination of the structure of tractable and intelligible reasoning in cognitive science and artificial intelligence. Working from the perspective of formal epistemology and cognitive science, Andreas uses structuralist notions from Bourbaki and Sneed to provide new foundational analyses of frames, object-oriented programming, belief revision, and truth maintenance. Andreas then builds on these analyses to construct a novel logic of tractable reasoning he calls frame logic, together with a novel belief revision scheme that is tractable for frame logic. Put together, these logical analyses and tractability results provide new understandings of dynamic and inferential reasoning. Jon Doyle, North Carolina State University |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
7.2.6.4 Updating the Epistemic Ranking |
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Online resource; title from digital title page (viewed on June 19, 2020) |
| Subject |
Reasoning.
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Logic.
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Artificial intelligence.
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Philosophy: logic.
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Applied mathematics.
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Neurosciences.
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Philosophy of mind.
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Computers -- Intelligence (AI) & Semantics.
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Philosophy -- Logic.
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Mathematics -- Applied.
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Medical -- Neuroscience.
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Philosophy -- Mind & Body.
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Logic
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Reasoning
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| Form |
Electronic book
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| ISBN |
9783030362331 |
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3030362337 |
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3030362353 |
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9783030362355 |
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