Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening are carefully controlled. Sequent calculus More about first order logic Thus far, we have two contrasting presentations of first order logic: as a system of derivations governed by introduction and elimination rules for the connectives and quantifiers, and as a semantic theory with an associated technique of analysis by semantic tableaux.

Logic in Logic Programming: Sequent Calculus, Higher-Orders, and Linear Logic Fourth International School for Computer Science Researchers Acireale, Sicily 29 June – 3 July 1992 Dale Miller Computer Science Department University of Pennsylvania Philadelphia, PA 19104–6389 USA dale@cis.upenn.edu Some corrections have been made on 5 July 1992. There is a set of propositions (although as remarked above, to be thought of more as resources to be acquired than as statements to be proved) which we construct through recursion . Linear logic lends itself to many different presentations, explanations and intuitions.

Linear logic is usually given in terms of sequent calculus. Linear logic as a sequent calculus Linear logic ignores the left/right-asymmetry of intuitionism; in particular, one can directly deal with right-handed sequents. The linear logic introduced in [3] by J.-Y. However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus. Linear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic.

Samuel R. Buss, in Studies in Logic and the Foundations of Mathematics, 1998. Girard keeps one of the so-called structural rules of the sequent calculus: the exchange rule.In a one-sided sequent calculus this rule can be formulated as. Intuitionistic Linear Logic (ILL) is the intuitionnistic restriction of linear logic: the sequent calculus of ILL is obtained from the two-sided sequent calculus of linear logic by constraining sequents to have exactly one formula on the right-hand side: .The connectives , and are not available anymore, but the linear … Linear logic, TCS 1987, Girard; Wiki-LL (Wikipedia-clone for linear logic maintained by ENS Lyon researchers) Olivier Laurent’s lecture notes about proof-nets (formal way of representing LL proofs as graphs) In this class: introduction, starting with cut elimination in classical logic. The first thing to do is to try to rewrite Linear logic familiar connpctiv.,s in this framework where sti=tusal rules have been limited to … We have developed the sequent calculus only for classical propositional logic; however, one of the advantages of the sequent calculus is its flexibility in being adapted for non-classical logics. 1.2.13 Some remarks.