Abstract. When defined with general elimination/application rules, natural deduction and λ-calculus become closer to sequent calculus. In order to get real isomorphism, normalisa...
We see cut-free sequent systems for the basic normal modal logics formed by any combination the axioms d, t, b, 4, 5. These systems are modular in the sense that each axiom has a c...
Abstract. We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existin...
act Completion (Full Version) Guillaume Burel Claude Kirchner August 6, 2007 Deduction Modulo implements Poincar´e’s principle by identifying deduction and computation as diff...
Abstract. We introduce a tree-sequent calculus for inquisitive logic (Groenendijk 2008) as a special form of labelled deductive system (Gabbay 1996). In particular, we establish th...