Let ‘P’ and ‘Q’ stand for (simple or compound) propositions.
The deduction theorem says that: if Q can be logically inferred from P, then ‘If P then Q’ can be proved as a theorem in the logical system in question.
This gives a method for dispensing with rules of inference in favor of axioms and theorems; but it does not hold for all logical systems, and in any case not all rules of inference can be dispensed with, for reasons due to Lewis Carroll.
Source:
L Carrol; What the Tortoise Said to Achilles
Table of Contents
- 1 Videos
- 2 Related Products
- 2.1 Advances in Natural Deduction: A Celebration of Dag Prawitz's Work (Trends in Logic)
- 2.2 The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
- 2.3 Logic and Discrete Mathematics: A Concise Introduction
- 2.4 Logic and Structure (Universitext)
- 2.5 First Course in Mathematical Logic (Dover Books on Mathematics)
- 2.6 Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)
- 2.7 What Is Mathematical Logic? (Dover Books on Mathematics)
- 2.8 Interpreting Biomedical Science: Experiment, Evidence, and Belief
- 2.9 Metalogic: An Introduction to the Metatheory of Standard First Order Logic
- 2.10 Upside-Down Meta-Interpretation of the Model Elimination Theorem-Proving Procedure for Deduction and Abduction
Videos
Advances in Natural Deduction: A Celebration of Dag Prawitz's Work (Trends in Logic)
- Hardcover Book
- English (Publication Language)
- 279 Pages - 03/03/2014 (Publication Date) - Springer (Publisher)
The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
- Amazon Kindle Edition
- Domingos, Pedro (Author)
- English (Publication Language)
- 338 Pages - 09/22/2015 (Publication Date) - Basic Books (Publisher)
Logic and Discrete Mathematics: A Concise Introduction
- Amazon Kindle Edition
- Conradie, Willem (Author)
- English (Publication Language)
- 428 Pages - 04/28/2015 (Publication Date) - Wiley (Publisher)
Logic and Structure (Universitext)
- Used Book in Good Condition
- van Dalen, Dirk (Author)
- English (Publication Language)
- 273 Pages - 11/13/2012 (Publication Date) - Springer (Publisher)
First Course in Mathematical Logic (Dover Books on Mathematics)
- Amazon Kindle Edition
- Suppes, Patrick (Author)
- English (Publication Language)
- 288 Pages - 04/30/2012 (Publication Date) - Dover Publications (Publisher)
Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)
- Dowek, Gilles (Author)
- English (Publication Language)
- 168 Pages - 01/13/2011 (Publication Date) - Springer (Publisher)
What Is Mathematical Logic? (Dover Books on Mathematics)
- Amazon Kindle Edition
- Crossley, J. N. (Author)
- English (Publication Language)
- 99 Pages - 08/29/2012 (Publication Date) - Dover Publications (Publisher)
Interpreting Biomedical Science: Experiment, Evidence, and Belief
- Amazon Kindle Edition
- Maiväli, Ülo (Author)
- English (Publication Language)
- 375 Pages - 06/12/2015 (Publication Date) - Academic Press (Publisher)
Metalogic: An Introduction to the Metatheory of Standard First Order Logic
- Hunter, Geoffrey (Author)
- English (Publication Language)
- 304 Pages - 06/26/1996 (Publication Date) - University of California Press (Publisher)
Upside-Down Meta-Interpretation of the Model Elimination Theorem-Proving Procedure for Deduction and Abduction
- Mark E. Stickel (Author)
- 04/19/1992 (Publication Date) - PN (Publisher)
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