Natural Deduction, Hybrid Systems and Modal Logics

1. Front Matter

   Pages i-xxiii

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2. Preliminaries

   • Andrzej Indrzejczak

   Pages 1-27

3. Standard Natural Deduction

   • Andrzej Indrzejczak

   Pages 28-74

4. Other Deductive Systems

   • Andrzej Indrzejczak

   Pages 75-94

5. Extended Natural Deduction

   • Andrzej Indrzejczak

   Pages 95-136

6. Survey of Modal Logics

   • Andrzej Indrzejczak

   Pages 137-181

7. Standard Approach to Basic Modal Logics

   • Andrzej Indrzejczak

   Pages 182-220

8. Beyond Basic Logics and Standard Systems

   • Andrzej Indrzejczak

   Pages 221-258

9. Labelled Systems in Modal Logics

   • Andrzej Indrzejczak

   Pages 259-296

10. Logics of Linear Frames

    • Andrzej Indrzejczak

    Pages 297-331

11. Analytic Labelled ND and Proof Search

    • Andrzej Indrzejczak

    Pages 332-362

12. Modal Hybrid Logics

    • Andrzej Indrzejczak

    Pages 363-397

13. Proof Methods for MHL

    • Andrzej Indrzejczak

    Pages 398-444

14. Back Matter

    Pages 445-491

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A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least some hints of what this book is about. The notion of natural deduction or modal logic are rather well known, but the notion of “hybrid system” certainly needs some explanation. In short, this study may be seen as a kind of search for good deductive systems. We think of systems good in practice which may be applied with easenotonlybywelltrainedlogiciansbutalso, forexample, byphilosophers who need handy deductive tools accompanying their analyses. In parti- lar, we are interested in providing systems that may be widely applied in teaching logic. Nowadays one may observe that several courses in “critical thinking” tend to eliminate courses in practical logic. On the other hand, logic is often taught as a strictly mathematical discipline in very dema- ing courses. It is important to ?ll the gap between these extrema, and the crucial ingredient of any course which is supposed to teach how to use logic, is certainly a suitable deductive system. Since we address this work to a wide audience interested in applications of logic, we were trying to make it self-contained and accessible to a reader with no hard training in logic. The assumed reader should have some ba- ground in logic (an elementary course covering classical propositional and ?rst-order logic with basics of set theory is enough) but not necessarily in modal logic.

• Classical logic
• Frames
• Hybrid logics
• Hybrid systems
• Natural deduction
• Proof theory
• Racter
• Resolution
• Temporal logics
• logic
• modal logic
• proving

• Dept. Logic, University of Lódz, Lódz, Poland

  Andrzej Indrzejczak

Andrzej Indrzejczak is professor of logic and Head of the Department of General Methodology at the University of Lodz, Poland. His scientific interests include the proof theory for non-classical logics, the philosophy of logic and the methodology of science. He is the author of three books and numerous papers concerned mainly with the investigation of proof techniques for non-classical logics, published e.g. in Bulletin of the Section of Logic, Logic Journal of the IGPL, Logic and Logical Philosophy, Logica Trianguli, and Studia Logica.

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