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Everything about Contraposition
Mathematical logic concept
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent negated and swapped. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ContrapositionA 5-minute orientation
- Skim a recent paper: Evidential Support and ContrapositionInfluential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contextsCited 58 times
- Go sideways: Inverse (logic)A closely related topic
- Go sideways: Converse (logic)A closely related topic
📖 Definitions
Noun The statement of the form "if not Q then not P", given the statement "if P then Q".
Noun Opposition; contrast.
🏆 Landmark papers (most cited)
Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts
Displaying and Deciding Substructural Logics 1: Logics with Contraposition
Rationality, transitivity, and contraposition
Meaning-preserving contraposition of natural language conditionals
Stability analysis of sampled-data systems via open-/closed-loop characteristic polynomials contraposition
Extending the Contraposition Property of Propositional Logic for Fuzzy Abduction
Fārābī and Avicenna on Contraposition
Contraposition in European and Indian Logic
🆕 Influential since 2022
Evidential Support and Contraposition
On Fuzzy Negations and Laws of Contraposition. Lattice of Fuzzy Negations
Characterizations of fuzzy implications by the laws of contraposition
Representations of the fuzzy implications satisfying the law of left or right contraposition
Correction to: Evidential Support and Contraposition
📚 Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
The Power of LogicFrances Howard-Snyder, Daniel Howard-Snyder · 2009
Introduction to automata theory, languages, and computationJohn E. Hopcroft, Jeffrey D. Ullman · 1979
Principles of logicGeorge Hayward Joyce · 1908
An elementary handbook of logicToohey, John Joseph · 1918
Socratic logicPeter Kreeft · 2003
How Things PersistKatherine Hawley · 2002
A Doubter's AlmanacEthan Canin · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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