Logic
What makes a conclusion follow logically from its premises?
A conclusion follows logically from premises when no way of reinterpreting the non-logical words makes the premises true and the conclusion false.
A conclusion follows logically from premises when it can be derived from them step by step by rules that fix what 'and', 'not' and 'if' mean.
Syllogistic analysis represents an inference through categorical premises and a conclusion so that its validity can be tested by figure and form.
Logical consequence is the relation that makes an argument deductively valid: if its premises hold, its conclusion cannot fail as a matter of logic. The central question is what explains that necessity and formality.
Model-theoretic accounts look for the absence of a countermodel. Proof-theoretic accounts look for a valid route from premises to conclusion. The two approaches often classify the same arguments as valid, but they explain validity in different terms.