valid,
adj. (Logic) 1. (of an inference or argument) a. also called sound. having premises and conclusion so related that whenever the former are true the latter must also be true.
b. often formally valid. so related where the inference is justified by the form of the premises and conclusion alone. Thus
Tom is a bachelor.
therefore Tom is unmarried.
is valid but not formally valid, while
today is hot and dry.
therefore today is hot.
is formally valid.2. (informally) correct. Often `valid' is used of the conclusion of an argument, but this is misleading, as the same conclusion can be both validly and invalidly inferred. Thus today is hot can be validly inferred as above, or invalidly inferred from today is hot or dry; consequently, validity cannot be said to attach to the conclusion by itself. Nor should the classification of arguments as valid or invalid be confused with the classification of component statements as true or false; all combinations of such classifications are possible with the sole exception that a valid argument cannot have both true premises and a false conclusion. 3. generally, (of a sentence in a formal language) true in every interpretation; satisfied by every assignment of values to the variables in every interpretation, so that every interpretation is a model for the statement. A sentence is valid in a theory if it is satisfiable in every model for the theory.
b. often formally valid. so related where the inference is justified by the form of the premises and conclusion alone. Thus
Tom is a bachelor.
therefore Tom is unmarried.
is valid but not formally valid, while
today is hot and dry.
therefore today is hot.
is formally valid.2. (informally) correct. Often `valid' is used of the conclusion of an argument, but this is misleading, as the same conclusion can be both validly and invalidly inferred. Thus today is hot can be validly inferred as above, or invalidly inferred from today is hot or dry; consequently, validity cannot be said to attach to the conclusion by itself. Nor should the classification of arguments as valid or invalid be confused with the classification of component statements as true or false; all combinations of such classifications are possible with the sole exception that a valid argument cannot have both true premises and a false conclusion. 3. generally, (of a sentence in a formal language) true in every interpretation; satisfied by every assignment of values to the variables in every interpretation, so that every interpretation is a model for the statement. A sentence is valid in a theory if it is satisfiable in every model for the theory.