A Logic of Modification and Creation

In this paper, MCL (modification and creation logic) is presented, a variant of quantified dynamic logic (QDL) with enhanced expressivity. In MCL, functions and predicates can be modified by actions f := λx.t and p := λx.φ, respectively, and new objects can be created by the action Create. This contrasts with QDL, where only the value assignments of variables can be modified. Models of MCL are collections of worlds which are locally models of first-order logic. There is an axiomatisation which is sound and complete. MCL is inspired on QDL and several other reasoning systems about the effect of actions, such as the specification language COLD, Gurevich's Abstract State Machines (formerly known as Evolving Algebras) and Dynamic Database Logic.