The survey paper A Survey of Linear Logic Programming may also be of interest. Two design goals of Forum Uniform proofs in linear logic. A logic programming language is then a logical system for which uniform proofs are complete.
G is a single formula.
A natural generalization requires that all possible introductions on the right can be done simultaneously. Although the sequent calculus cannot deal directly with simultaneous rule application, reference to permutabilities of inference rules can indirectly address simultaneity. Forum was the result of applying this definition to linear logic. Merging two different threads of logic programming languages. Naturally, it would be nice to find one logic programming language that incorportated both abstractions and concurrency.