Sound argument in logic: meaning and examples

A sound argument is a valid argument whose premises are all actually true. Soundness adds a claim about the world to a claim about form, so a truth table can establish only half of it.

Validity is a property of the pattern: in every row where the premises hold, the conclusion holds. Soundness adds that the premises hold in the real case, the one row that actually obtains. A sound argument therefore has a true conclusion, which is why soundness is what anyone offering an argument is ultimately claiming. The two words are kept apart in every logic course because they fail in different ways: an invalid argument has a bad form, an unsound valid argument has a false premise.

The artefact on this page is the same modus ponens used for validity: premises A -> B and A, conclusion B, 4 rows. The validity check holds; no admissible assignment makes every premise true and the conclusion false. The premise-consistency check holds with the witness A = TRUE, B = TRUE, which shows that the premises can be true together. Whether they are true, whether A really holds and really brings B with it, is not a question any row of the table answers; that is the part of soundness that stays with the person making the argument.

In practice the distinction separates two kinds of review. Checking a rule's logic (does the conclusion follow from the stated conditions?) is a validity question the engine settles exactly. Checking its inputs (is this customer really a member, is this sensor reading right?) is a soundness question that belongs to data and to the domain expert. The term is confused with validity itself, and “sound” is sometimes used loosely for “reasonable”, which is weaker than either.

Example

p1 — A -> B · premisep2 — 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 = T, B = T · Exhaustively checked and solver cross-checked · 4 rows

Truth table (4 rows)

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

Plain-language reading

BeginnerConclusion: B is true.

IntermediateConclusion: B is true.

AdvancedConclusion: B is true.
Formal notation: B

The common slip

Expecting a logic tool to tell you an argument is sound. It can show validity and premise consistency on every row; the truth of the premises is a fact about the world, and no table contains it. “Valid” on the page is not a claim that the premises are true.

Questions

Can an argument be sound but invalid?

No. Soundness includes validity by definition. An argument with true premises and a true conclusion but a bad form, such as affirming the consequent, is invalid and therefore unsound, even though everything in it happens to be true.

Guides

Valid vs sound arguments

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.