Routledge Dictionary of Language and Linguistics
equivalence (also biconditional, bilateral implication)
In formal logic the conjunction of two elementary propositions p and q that is true if and only if both parts of the sentence have the same truth value (notation: p≡q or p↔q). This relation is represented in the (two-place) truth table:
| p | q | p↔q |
| t | t | t |
| t | f | f |
| f | t | f |
| f | f | t |
Equivalence refers to the two-place sentence operator if p, then q as well as the propositional connective defined by it.
The equivalence corresponds to bilateral implication, i.e. both p→q and q→p are valid: Ralph is Philip ‘s father→ Philip is Ralph ‘s son and vice versa. In everyday usage, equivalences correspond to paraphrases like p, if and only if q or p is a necessary and sufficient condition for q, in which case it frequently remains ambiguous as to whether it is a matter of equivalence or of implication. In the framework of lexical semantics (
meaning, semantics) equivalence corresponds to the conventional truth-functional semantic relation of synonymy.
References
formal logic
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