logical implication
[ˈlɑːdʒɪkəl ˌɪmpləˈkeɪʃən]
nounpl: logical implications
implicação lógica
1. A relationship between two propositions where if the first is true, the second must also be true; the logical consequence or entailment of a statement
The logical implication of 'all humans are mortal' and 'Socrates is human' is 'Socrates is mortal'.
A implicação lógica de 'todos os humanos são mortais' e 'Sócrates é humano' é 'Sócrates é mortal'.
2. In formal logic, a conditional statement (if P then Q) that establishes a truth relationship between antecedent and consequent
The logical implication P → Q is false only when P is true and Q is false.
A implicação lógica P → Q é falsa apenas quando P é verdadeira e Q é falsa.
This is primarily a technical and academic term used in philosophy, mathematics, computer science, and formal logic courses. It is used identically in both Brazilian and American English-speaking academic contexts, and similarly across Portuguese-speaking regions. The term is not part of colloquial speech and remains within specialized discourse communities.
Related Idioms & Phrases
the logical implication follows that
draw a logical implication
logical implication entails
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