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 The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age
- 2.2 The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
- 2.3 Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra
- 2.4 Implicative and Disjunctive Prevarieties: Algebraic aspects of Deduction Theorem
- 2.5 Markov Models: Introduction to Markov Chains, Hidden Markov Models and Bayesian networks (Advanced Data Analytics Book 3)
- 2.6 Automated Deduction - CADE-14: 14th International Conference on Automated Deduction, Townsville, North Queensland, Australia, July 13 - 17, 1997, Proceedings (Lecture Notes in Computer Science)
- 2.7 Logic and Structure (Universitext)
- 2.8 First Course in Mathematical Logic (Dover Books on Mathematics)
- 2.9 What Is Mathematical Logic? (Dover Books on Mathematics)
- 2.10 Advances in Natural Deduction: A Celebration of Dag Prawitz's Work (Trends in Logic)
Videos
The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age
- Princeton University Press
- Hardcover Book
- von Plato, Jan (Author)
- English (Publication Language)
- 400 Pages - 08/02/2017 (Publication Date) - Princeton University Press (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)
Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra
- Pynko, Dr. Alexej P. (Author)
- English (Publication Language)
- 68 Pages - 01/01/2019 (Publication Date) - Independently published (Publisher)
Implicative and Disjunctive Prevarieties: Algebraic aspects of Deduction Theorem
- Pynko, Dr. Alexej P. (Author)
- English (Publication Language)
- 113 Pages - 09/12/2019 (Publication Date) - Independently published (Publisher)
Automated Deduction - CADE-14: 14th International Conference on Automated Deduction, Townsville, North Queensland, Australia, July 13 - 17, 1997, Proceedings (Lecture Notes in Computer Science)
- McCune, William (Author)
- English (Publication Language)
- 462 Pages - 01/15/1997 (Publication Date) - Springer (Publisher)
Logic and Structure (Universitext)
- Amazon Kindle Edition
- van Dalen, Dirk (Author)
- English (Publication Language)
- 276 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)
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)
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)
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