Conditional and Preferential Logics Proof Methods and Theorem Proving 1st Edition by Gian Luca Pozzato ISBN 1607500957 9781607500957

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ISBN 10: 1607500957
ISBN 13: 9781607500957
Author: Gian Luca Pozzato

explores advanced logical frameworks, focusing on conditional logics and preferential logics, which are essential for reasoning in uncertain or non-monotonic contexts. The book delves into proof methods and theorem-proving techniques for these logics, providing a thorough examination of both theoretical foundations and practical applications. Pozzato presents various proof systems, algorithms, and computational methods to handle conditional and preferential statements, offering valuable insights for those working in artificial intelligence, formal reasoning, and non-classical logics. The work is aimed at researchers and students interested in expanding their understanding of non-monotonic reasoning and formal logic systems.

Conditional and Preferential Logics Proof Methods and Theorem Proving 1st Edition Table of contents:

Part I: Foundations of Conditional and Preferential Logics

2. Conditional Logics: Concepts and Basic Structures

   • What is Conditional Logic?
   • Formalization of Conditional Statements
   • Syntax and Semantics of Conditional Logics
   • Possible Worlds Semantics in Conditional Logics
   • Applications of Conditional Logics in AI and Reasoning Systems

3. Preferential Logics: Fundamentals and Development

   • Understanding Preferential Reasoning
   • Formal Models of Preferential Logics
   • Semantics of Preferential Logics
   • Relation to Classical and Non-Monotonic Logics
   • Preferential Reasoning in Decision Theory

4. Basic Proof Methods in Conditional and Preferential Logics

   • Natural Deduction Systems for Conditional Logics
   • Tableaux and Sequent Calculus Methods
   • Axiomatic Systems and Proof Strategies
   • Comparison of Proof Methods in Classical vs. Conditional and Preferential Logics

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Part II: Theorem Proving Techniques

5. Automated Theorem Proving in Conditional Logics

   • Overview of Automated Theorem Proving Approaches
   • Implementing Proof Systems for Conditional Logics
   • Soundness and Completeness of Proof Methods
   • Decision Procedures for Conditional Logics
   • Case Studies in Automated Theorem Proving for Conditional Logics

6. Preferential Theorem Proving: Challenges and Solutions

   • Theorem Proving in Preferential Logics
   • Methods for Handling Inconsistent and Partial Information
   • Non-Monotonic Inference and Preferential Proof Systems
   • Algorithms for Preferential Reasoning
   • Complexity Issues in Preferential Theorem Proving

7. Proof Search and Optimization Techniques

   • Proof Search Algorithms for Conditional and Preferential Logics
   • Improving Efficiency of Proof Search
   • Optimizing Proof Search in Theorem Proving Systems
   • Case Studies in Proof Search for Conditional and Preferential Logics
   • Practical Implementations and Tools

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Part III: Advanced Topics in Conditional and Preferential Logics

8. Non-Monotonic Reasoning in Conditional and Preferential Logics

   • The Nature of Non-Monotonic Reasoning
   • Conditional and Preferential Logics as Non-Monotonic Systems
   • Applications in AI and Cognitive Science
   • Methods for Handling Exceptions and Defeasible Reasoning

9. Conditional Logics and Belief Revision

   • The Link Between Conditional Logics and Belief Revision Theory
   • Formalizing Belief Updates and Modifications
   • Preferential Approaches to Belief Revision
   • Algorithmic Solutions for Dynamic Knowledge Updates

10. Multi-Agent Systems and Conditional/Preferential Logics

    • Applications of Conditional and Preferential Logics in Multi-Agent Systems
    • Reasoning About Knowledge and Belief in Multi-Agent Systems
    • Coordination and Decision Making in Multi-Agent Systems
    • Examples and Applications of Preferential Reasoning in Multi-Agent Contexts

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Part IV: Applications and Case Studies

11. Conditional and Preferential Logics in Artificial Intelligence

    • AI Applications of Conditional and Preferential Reasoning
    • Expert Systems and Knowledge Representation
    • Machine Learning and Reasoning with Incomplete Information
    • Conditional and Preferential Logics for Problem Solving in AI

12. Applications in Decision Theory and Ethics

    • Using Preferential Logics for Decision-Making Processes
    • Conditional Reasoning in Ethical Dilemmas
    • Formalizing Ethical Principles Using Conditional Logics
    • Practical Applications in Decision Theory and Ethics

13. Case Studies: Implementing Conditional and Preferential Logics

    • Real-World Implementations of Conditional Logics in Software
    • Integrating Preferential Logics in Knowledge-Based Systems
    • Case Study 1: Automated Legal Reasoning
    • Case Study 2: Conditional Logics in Robotics
    • Case Study 3: Preferential Logics in Game Theory

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Conclusion
14. Summary and Future Directions in Conditional and Preferential Logics
– Key Takeaways from the Book
– Open Problems and Challenges in Conditional and Preferential Reasoning
– Emerging Trends in Non-Classical Logics and Their Applications
– Future Research Directions

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