Deductive reasoning Deductive reasoning Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true. Deductive reasoning (""top-down logic"") contrasts with inductive reasoning (""bottom-up logic"") in the following way; in deductive reasoning, a conclusion is reached reductively by applying general rules which hold over the entirety of a
Logical equivalence if and only if formula_2'". In particular, the truth value of formula_7 can change from one model to another. The claim that two formulas are logically equivalent is a statement in the metalanguage, expressing a relationship between two statements formula_1 and formula_2. The statements are logically equivalent if, in every model, they have the same truth value. Logical equivalence In logic, statements formula_1 and formula_2 are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model (Mendelson 1979:56). The logical equivalence of formula_1 and formula_2 is sometimes expressed as