
 Linear Logic (Stanford Encyclopedia of Philosophy) 
  In the sequent calculus presentation of classical logic, the rules for the connectives "and" and "or", as well as the Cut rule and the rule for implication may be presented equivalently in an additive form (the context of the premises are the same) or a multiplicative form (the context of the premises are different). 
  Logic, or at least prooftheory, is focused on formal proof systems: intuitionistic predicate calculus, classical predicate calculus, arithmetics, higher order calculi, and a wealth of similar consistent and structured sets of processbuilding rules. 
  Many models of linear logic proofs have been proposed; we consider that, to date, the simplest and most intuitive construction is those based on the socalled “relational semantics”, where formulas are interpreted as multisets, sequents as tuples of multisets and proofs as relations over the interpretation of sequents. 
 plato.stanford.edu /entries/logiclinear (5958 words) 
