منابع مشابه
Algebraic proofs of cut elimination
Algebraic proofs of the cut-elimination theorems for classical and intuitionistic logic are presented, and are used to show how one can sometimes extract a constructive proof and an algorithm from a proof that is nonconstructive. A variation of the double-negation translation is also discussed: if φ is provable classically, then ¬(¬φ) is provable in minimal logic, where θ denotes the negation-n...
متن کاملAlgebraic Aspects of Cut Elimination
We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of...
متن کاملModular Cut-Elimination: Finding Proofs or Counterexamples
Modular cut-elimination is a particular notion of ”cut-elimination in the presence of non-logical axioms” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cut-elimination for standard calculi, a wide class of (possibly) multipleconclusion sequent calculi with generalized quantifiers. We provide a ”universal” modular c...
متن کاملCuts for circular proofs: semantics and cut-elimination
One of the authors introduced in [16] a calculus of circular proofs for studying the computability arising from the following categorical operations: finite products, finite coproducts, initial algebras, final coalgebras. The calculus presented [16] is cut-free; even if sound and complete for provability, it lacked an important property for the semantics of proofs, namely fullness w.r.t. the cl...
متن کاملClassical Proofs as Programs, Cut Elimination as Computation
We show that the SN and CR cut-elimination procedure on Gentzen-style classical logic LKT/LKQ, as presented in Danos et al.(1994), is isomorphic to call-by-name (CBN) and call-by-value (CBV) reduction system respectively. Our method is simple. We assign typed -terms on intuitionistic decoration of LKT/LKQ so as to simulate the cut-elimination procedure by -contraction | i.e. we simulate cutelim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Logic and Algebraic Programming
سال: 2001
ISSN: 1567-8326
DOI: 10.1016/s1567-8326(01)00009-1