Automated Generation of Analytic Calculi for Logics with Linearity

Abstract. We show how to automatically generate analytic hypersequent calculi for a large class of logics containing the linearity axiom (lin) (A ⊃ B) ∨ (B ⊃ A) starting from existing (single-conclusion) cut-free sequent calculi for the corresponding logics without (lin). As a corollary, we define an analytic calculus for Strict Monoidal T-norm based Logic SMTL.

Automated Generation of Analytic Calculi for Logics with Linearity

Abstract. We show how to automatically generate analytic hypersequent calculi for a large class of logics containing the linearity axiom (lin) (A oe B). (B oe A) starting from existing (single-conclusion) cut-free sequent calculi for the corresponding logics without (lin). As a corollary, we define an analytic calculus for Strict Monoidal T-norm based Logic SMTL. 1 Introduction A central task of logic in computer science is to provide automated generationof suitable analytic calculi for a wide range of non-classical logics. By analytic calculi we mean calculi in which the proof search proceeds by step-wise decompo-sition of the formula to be proved. The most famous examples of such calculi are the Gentzen sequent calculus LK and its single-conclusion version LJ for classi-cal and intuitionistic logic respectively. Cut-free "Gentzen-style " calculi serve as a basis for automated deduction, and allow the extraction of important implicitinformation from proofs such as numerical bounds and programs in proof-style. The presence of the linearity axiom (lin) (A oe B). (B oe A) in the Hilbert-style axiomatization of a logic ensures a total ordering among the elements of its intended models (e.g., Kripke structures, truth-value interpretations). Severallogics have been defined adding