A Semantics for a Class of Stratified Production System Programs

We present our research on defining a correct semantics for forward chaining production systems (PS) programs. A correct semantics must ensure that the execution of the program is deterministic and that it will terminate. We define a class of function-free stratified PS programs, and develop a fixpoint semantics and a declarative semantics for these programs. A stratified PS program comprises an initial extensional database (EDB init) of facts, and a set of productions. We define the conditions for the productions in the PS program to be stratified and we define an operator TPS, which computes the fixpoint for the productions of the stratified PS program. The fixpoint is represented by an updated database EDBn. A corresponding logic program PS dd is derived from the stratified PS program. PS dd is stratified and has a standard minimal model MPS dd. The declarative semantics for the PS program is given by this model MPS dd. We prove that the declarative semantics given by the model MPS dd for PS dd is equivalent to the fixpoint EDBn for the productions in the PS program.