succedentused

Succedentused is a term that occasionally appears in discussions of sequent calculus and related proof-theoretic formalisms. It denotes a methodological emphasis on the succedent, the right-hand side of a sequent, i.e., the formulas considered as conclusions that follow from a given set of antecedents.

In a sequent Γ ⊢ Δ, where Γ is the antecedent and Δ the succedent, succedentused refers to practices that prioritize analysis, manipulation, or selection of formulas within Δ during proof construction. Proponents argue that focusing on the succedent can illuminate which conclusions are most directly supported by the premises and which rules are most effective at deriving them.

In multi-succedent systems, where Δ may contain several formulas, succedentused may guide rule application by selecting particular elements of Δ to aim for or by tracking how different succedents interact under inference. Critics caution that overemphasis on the right-hand side can obscure the role of the antecedent.

Etymology reflects its composition from succedent, the term for the right side of a sequent, and used, indicating a user-guided or practice-oriented approach. The term is not part of standard, widely cited terminology and remains informal and regional in scope.

See also: sequent calculus, succedent, antecedent, multi-succedent logic.