logical

Logical is an adjective relating to logic, the systematic study of the principles of correct reasoning and valid inference. In philosophy, mathematics, computer science, and related fields, logical analysis aims to distinguish arguments that are structurally valid from those that are fallacious, regardless of their content. An argument is logical if its conclusion follows from its premises by acceptable rules of inference; a valid argument preserves truth from premises to conclusion, and a sound argument is both valid and with true premises.

Logic covers a range of topics and approaches. Formal logic studies the formal structure of arguments using symbolic language, including deductive systems such as propositional logic, predicate logic (first-order logic), and, in some traditions, higher-order logics. Informal logic examines everyday argumentative reasoning, focusing on quality and persuasiveness rather than purely symbolic form. Within formal logic, subfields include truth-functional reasoning, quantification, modal logic (necessity and possibility), and other non-classical logics that address time, knowledge, obligation, or possibility.

Historically, logic originated with Aristotle’s syllogistic and evolved through Frege’s predicate calculus, Boole’s algebra of logic, and the foundational work of Russell and Whitehead. In the 20th century, Hilbert-style axiomatic methods and varying semantic theories deepened the field, influencing computer science, mathematics, and linguistics.

Applications of logical methods include proving theorems, verifying software correctness, designing algorithms, and evaluating arguments in philosophy and public discourse. Logical reasoning underpins critical thinking, enabling analysis of validity, consistency, and coherence in diverse domains.