  The overall goal of this paper is to investigate the theoretical foundations
of algorithmic verification techniques for first order linear logic
specifications. The fragment of linear logic we consider in this paper is based
on the linear logic programming language called LO enriched with universally
quantified goal formulas. Although LO was originally introduced as a
theoretical foundation for extensions of logic programming languages, it can
also be viewed as a very general language to specify a wide range of
infinite-state concurrent systems.
  Our approach is based on the relation between backward reachability and
provability highlighted in our previous work on propositional LO programs.
Following this line of research, we define here a general framework for the
bottom-up evaluation of first order linear logic specifications. The evaluation
procedure is based on an effective fixpoint operator working on a symbolic
representation of infinite collections of first order linear logic formulas.
The theory of well quasi-orderings can be used to provide sufficient conditions
for the termination of the evaluation of non trivial fragments of first order
linear logic.
