Premise in logic: meaning and examples

A premise is a statement an argument takes as given. The conclusion is what is claimed to follow from the premises taken together, and validity is tested only on the rows where every premise is true.

An argument has one or more premises and exactly one conclusion. The premises are not assumed true in the world; they are the conditions under which the conclusion is claimed. In the engine's argument mode each premise is a formula in its own column, and the validity check looks only at the rows where all those columns read true. Premises play the same role that assumptions play in decision mode, with one difference: assumptions restrict which rows are admissible at all, while premises are the “if” part of the claim being tested.

The artefact on this page is the disjunctive syllogism: premises A OR B and NOT A, conclusion B, 4 rows. The first premise column reads false, true, true, true and the second true, true, false, false, so the only row where both premises are true is row 1, A = FALSE, B = TRUE, and there the conclusion is true. The validity check holds. The premise-consistency check holds with that same row as its witness: the premises can be true together, so the validity is not vacuous.

Premises matter in practice because they are where arguments usually go wrong. A policy that reads “members and invited guests may enter unless banned” has three premises hiding in one sentence, and a reviewer's first job is to list them. In a philosophy course, identifying premises and conclusion is the first step of every exercise. The term is confused with an assumption (a constraint on the domain rather than a step in the argument) and with a hypothesis, which in logic means the antecedent of a conditional.

Example

p1 — A OR B · premisep2 — NOT A · premiseconclusion — B · conclusion

Exact checks

Does the conclusion follow from the premises? Yes · Exhaustively checked and solver cross-checked · 4 rows

Can all premises be true together? Yes Example assignment: A = F, B = T · Exhaustively checked and solver cross-checked · 2 rows

Truth table (4 rows)

Premise in logic: meaning and examples
#	A	B	p1	p2	conclusion
0	FALSE	FALSE	FALSE	TRUE	FALSE
1	FALSE	TRUE	TRUE	TRUE	TRUE
2	TRUE	FALSE	TRUE	FALSE	FALSE
3	TRUE	TRUE	TRUE	FALSE	TRUE

Plain-language reading

BeginnerConclusion: B is true.

IntermediateConclusion: B is true.

AdvancedConclusion: B is true.
Formal notation: B

The common slip

Treating a premise as something the argument has established. Premises are inputs, not results; a valid argument with a false premise proves nothing about its conclusion. The consistency check tells you whether the premises can all hold, not whether they do.

Questions

What happens if I add a premise that contradicts the others?

No row has all premises true, so there is no counterexample and every conclusion follows vacuously. The engine reports the argument valid, marks it vacuous, and the premise-consistency check reports the premises inconsistent. The glossary page on vacuous truth shows this.

Practice

Argument validity exercises with answers

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.