Antecedent in logic: meaning and examples

The antecedent is the “if” part of a conditional: in A -> B, A is the antecedent and B the consequent. A conditional is false only when its antecedent is true and its consequent false.

In “if it rains, the ground is wet”, the antecedent is “it rains”. The word comes from Latin for “going before”, and in the arrow notation it is always the left side, whatever order the sentence used: “the ground is wet if it rains” has the same antecedent. The antecedent is a sufficient condition for the consequent, and the consequent a necessary condition for the antecedent; keeping those two roles straight is most of what a conditional means.

The artefact on this page is A -> B itself. Its 4-row table reads true, true, false, true: the only false row is row 2, A = TRUE, B = FALSE, where the antecedent holds and the consequent does not, and that row is the counterexample of the tautology check. On rows 0 and 1 the antecedent is false and the conditional is true regardless of B, as the engine's reading states: when the “if” part is false, the condition is satisfied whatever the “then” part is. The satisfiable check holds with the witness A = FALSE, B = FALSE.

Antecedents matter in rule writing because a rule's trigger is its antecedent, and a rule with a never-true antecedent never fires yet never fails: that is vacuous truth. In a logic course, affirming the antecedent is modus ponens, the valid form, and denying it is a fallacy. The term is confused with the premise of an argument (a whole statement, not half of one) and with a cause; a conditional asserts no causal link.

Example

f := A -> B · output

Exact checks

Always true (tautology)? No Counterexample: A = T, B = F · Exhaustively checked and solver cross-checked · 3 rows

Always false (contradiction)? No Counterexample: A = F, B = F · Exhaustively checked and solver cross-checked · 1 rows

Can be true? Yes Example assignment: A = F, B = F · Exhaustively checked and solver cross-checked · 1 rows

Truth table (4 rows)

Antecedent in logic: meaning and examples
#	A	B	f
0	FALSE	FALSE	TRUE
1	FALSE	TRUE	TRUE
2	TRUE	FALSE	FALSE
3	TRUE	TRUE	TRUE

Plain-language reading

Beginnerf is true exactly when the following holds: if A is true, then B is true.
In every other case, f is false.
About the operators:
- An “if … then” condition only constrains the case where its “if” part holds: when the “if” part is false, the condition is satisfied whatever the “then” part is. It does not say the reverse.

Intermediatef is true exactly when the following holds: if A is true, then B is true.
In every other case, f is false.

Advancedf is true exactly when the following holds: if A is true, then B is true [material implication →].
In every other case, f is false.
Formal notation: A → B

The common slip

Inferring the consequent is false from the antecedent being false. A -> B with A = FALSE is true for both values of B, so nothing follows about B; that inference is the fallacy of denying the antecedent, and the worked example of that name shows its counterexample row.

Questions

Is the antecedent always written first?

In the arrow notation, yes: the antecedent is the left operand of ->. In prose it can come second, as in “B, provided that A”, and “A only if B” makes B the consequent. The pitfall page on arrow variants covers the notations.

Glossary

Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build 2026-11-07. Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.