The Method of Socratic Proofs
Springer International Publishing (Verlag)
978-3-031-82450-0 (ISBN)
This book contains a systematic and formal attempt to model solutions to problems such as: Is it possible to prove a question? Is it possible to prove something by the use of questions? Do the existing paradigms in the logic of questions allow one to combine questions and proofs? What are the results in this field? In developing answers, the book focuses on the applications of the method of Socratic proofs, and goes beyond that.
It starts out with an overview of the leading paradigms, issues, problems and ready solutions in the logic of questions, and places Inferential Erotetic Logic and the method of Socratic proofs against a wider background. It then introduces these two methods in more detail and explains how they can be used for classical logic, intuitionistic propositional logic and for basic modal logics. Next, the book deals with issues specific to the field of the logic of questions, introducing the tools of Minimal Erotetic Semantics (MiES). The final chapters describe the translations between proof systems: from a Socratic transformation, derived in an erotetic calculus, into a sequent system.
Chapter 1: Between the logic of questions and proof theory. An overview.- Chapter 2: Erotetic calculi for classical logic.- Chapter 3: Erotetic calculi for intuitionistic and modal logics.- Chapter 4: Erotetic calculi are calculi of questions.- Chapter 5: From erotetic calculi to proofs. The classical case.- Chapter 6: From erotetic calculi to proofs.
| Erscheinungsdatum | 16.06.2025 |
|---|---|
| Reihe/Serie | Trends in Logic |
| Zusatzinfo | XIX, 348 p. 20 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
| Geisteswissenschaften ► Philosophie ► Logik | |
| Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Schlagworte | Both-sided calculus EPQ • Erotetic calculi are calculi of questions • Erotetic calculi for classical logic • Erotetic calculi for intuitionistic and modal logics • Erotetic rules for the classical case • From erotetic calculi to proofs. The classical case • Inferential Erotetic Logic • intuitionistic and modal cases of erotetic calculi to proofs • Logic of Questions • Proof-search in erotetic calculi for FOL • Questions and problem-solving strategies in logic • questions and systems of questions in logic • Rules of intuitionistic and modal erotetic calculi • Sequent Systems for Intuitionistic Logic • Sequent Systems for Modal Logics • Socratic Proofs • Soundness and completeness in the intuitionistic and modal cases • Supplementing languages with sequents and questions • the classical case of erotetic calculi to proofs • Translations Between Proof Systems |
| ISBN-10 | 3-031-82450-4 / 3031824504 |
| ISBN-13 | 978-3-031-82450-0 / 9783031824500 |
| Zustand | Neuware |
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