The Semantics of Constraint Addition in Non-Linear Planning

The theory of non-linear planning was presented in a semi-formal way by Chapman in his seminal paper. He did not provide a fully formal axiomatisation of his theory, and many of his proofs were semantic rather than formal in nature. Consequently his theory does not exist in a form amenable to veriication using automated proof-checking technology. Further, it does not exist in a form which facilitates comparison with other formal theories. This paper provides a formalisation and interpretation of the underlying modal system and constraint-addition mechanism upon which the theory depends. The formal semantics of the modal system is used to justify supplementing an axiomatisation of the theory with a powerful axiom which replaces Chapman's informal proofs of temporal, codesignation and non-codesignation consistency. The addition of this axiom is required to allow the fully formal development of the remainder of Chapman's theory.