Rozprawa z dziedziny logiki erotetycznej, prezentująca skuteczne zastosowanie metody dowodów sokratycznych dla wybranej klasy normatywnych logik modalnych.

The book concerns the method of Socratic proofs for normal modal propositional logics: K, D, T, KB, K4, S4 and S5. The method of Socratic proofs is a method of solving logical problems by transforming questions expressing these problems. At the same time it is a methodology of formalizing logics in the framework of the so-called erotetic calculi (from gr. erotema - question). The method is grounded in Inferential Erotetic Logic.

Introduction

Chapter 1. The Method of Socratic Proofs for Classical Prepositional Calculus

1.1. Notation

1.2. Erotetic Calculus E*

1.2.1. Language L*

1.2.2. The Rules of E*

1.2.3. Semantical Invertibility of Rules

1.3. A Right-Sided Approach: Calculus E**

1.3.1. Language L** and the Rules of E**

1.3.2. Semantical Invertibility - Semantical Duality

1.4. The Method of Socratic Proofs and Inferential Erotetic Logic

Chapter 2. Erotetic Calculi for Normal Modal Prepositional Logics

2.1. Language M*

2.1.1. Syntax of M*

2.1.2. A Bit of Semantics

2.1.3. Questions of M*: An Intuitive Account of Socratic Transformations

2.2. The Rules of Calculi EL. Socratic Transformations via the Rules of EL

2.2.1. Calculus EK

2.2.2. Calculi EL

2.3. Semantical Invertibility of the Rules of EL. Soundness

2.4. Modal Erotetic Calculi and Inferential Erotetic Logic

Chapter 3. Completeness of Modal Erotetic Calculi

3.1. Paths of Socratic Transformations

3.2. Permanently Unsuccessful Sequents

3.3. Complete Socratic Transformations

3.4. Countermodels

Chapter 4. Related Work

4.1. Sequent Calculi

4.2. Tableau Systems

4.3. Rasiowa-Sikorski Deduction Systems

4.4. Natural Deduction

4.5. Labelled Deductive Systems

Final Remarks

Appendix

References

List of symbols

Index of names

Subject index