Dynamic Tractable Reasoning

Dynamic Tractable Reasoning
Author: Holger Andreas
Publisher: Springer Nature
Total Pages: 236
Release: 2020-03-27
Genre: Philosophy
ISBN: 3030362337

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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

Tractable Reasoning in Incomplete First-order Knowledge Bases

Tractable Reasoning in Incomplete First-order Knowledge Bases
Author: Yongmei Liu
Publisher:
Total Pages: 360
Release: 2006
Genre:
ISBN: 9780494157602

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In order to specify a limited reasoning service for proper+ KBs, we propose a new logic of limited belief called the subjective logic SL . SL supports unit resolution, but only does case analysis in a limited way. We give a sound and complete axiomatization for propositional SL . Reasoning based on SL is classically sound and is also classically complete in some simple cases. We show that SL -based reasoning with proper+ KBs is decidable in general, and tractable when both the KB and the query use a bounded number of variables. This thesis proposes a general methodology to establish tractable (by "tractable" we mean "solvable in polynomial time") limited reasoning services for incomplete first-order knowledge bases (KBs). It consists of defining a logic that is weaker than classical logic and has two properties: first, the entailment problem can be reduced to the model checking problem for a characteristic model; and second, the model checking problem is tractable for formulas with a bounded number of variables. We show this methodology in action for two forms of incomplete first-order KBs proposed by Levesque and Lakemeyer. One is called proper KBs, and is used for open-world reasoning. The other is called proper+ KBs, and is used for reasoning with disjunctive information. Levesque has proposed a reasoning scheme called V for proper KBs that is classically sound and is also classically complete when the query is in a certain normal form called NF . We prove that V is tractable for queries with a bounded number of variables. We also settle the open problems concerning the expressiveness and succinctness of NF . Then we extend V to reasoning in dynamic systems, and propose a tractable, sound, and sometimes complete solution to the projection problem, that is, determining whether a formula holds after a sequence of actions is performed.

Tractable Reasoning with Quality Guarantee for Expressive Description Logics

Tractable Reasoning with Quality Guarantee for Expressive Description Logics
Author: Yuan Ren (Ph.D.)
Publisher:
Total Pages: 0
Release: 2014
Genre: Description logics
ISBN:

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As a whole, the thesis develops a worst-case tractable, guaranteed sound, conditionally complete and empirically high-recall reasoning solution for both static and dynamic ontologies in expressive DLs. Some techniques presented in the thesis can also be used to improve the performance and/or completeness of other existing reasoning solutions. The results can further be generalised and extended to support a wider range of knowledge representation formalisms, especially when a consequence-based algorithm is available.

Author:
Publisher: IOS Press
Total Pages: 7289
Release:
Genre:
ISBN:

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Dynamic Epistemic Logic

Dynamic Epistemic Logic
Author: Hans van Ditmarsch
Publisher: Springer Science & Business Media
Total Pages: 303
Release: 2007-05-06
Genre: Philosophy
ISBN: 140205839X

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Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

A Dynamic Analysis of Reasoning

A Dynamic Analysis of Reasoning
Author: Cornelis Franciscus Martinus Vermeulen
Publisher:
Total Pages: 84
Release: 1989
Genre:
ISBN:

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Johan van Benthem on Logic and Information Dynamics

Johan van Benthem on Logic and Information Dynamics
Author: Alexandru Baltag
Publisher: Springer
Total Pages: 1072
Release: 2014-08-27
Genre: Philosophy
ISBN: 3319060252

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This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations.

ECAI 2008

ECAI 2008
Author: European Coordinating Committee for Artificial Intelligence
Publisher: IOS Press
Total Pages: 972
Release: 2008
Genre: Computers
ISBN: 1586038915

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Includes subconference "Prestigious Applications of Intelligent Systems (PAIS 2008)."