A Linear Logic Semantics for Object-Oriented, Deductive and Active Databases

Girard's linear logic [18] provides powerful means for studying state transformations and resource consumption in computations within a completely logical framework. The starting point of this work is Forum [22, 23], a presentation of higher order linear logic which is an abstract logic programming language[24], i.e., complete with respect to uniform proofs (cut-free and goal-directed proofs). A subset of Forum's formulas which form the logic programming language E hhf [11, 13], have been isolated and proved to be well-suited to encode a notion of state into sequents and proofs, to model state updates, and to provide constructs for parallel execution. In this paper, we will show how it is possible, using the language E hhf , to define a clean and simple semantics for object-oriented, deductive and active databases in a completely logical setting, that accounts for the various aspects of computation. In order to do this, we will briefly describe the semantics of Chimera [9, 1..