🤖 AI Summary
This work addresses the E-unification problem for non-ground terms in the presence of dynamically evolving sets of ground equations and inequations. It proposes a dynamic E-unification method that employs superposition calculus to saturate non-ground equations modulo a ground equational theory and introduces instantiation rules to match non-ground terms with ground terms, thereby enabling dynamic updates to the ground theory. To support this framework, the authors design a term ordering modulo theory that satisfies weak monotonicity and the subterm property, and they provide orientable inference rules for finite data structures—such as lists equipped with length and concatenation operations. The method is proven complete and capable of modeling evolving systems within quantified SMT problems.
📝 Abstract
We present an E-unification procedure for a set of non-ground (dis)equations, along with a dynamic set of ground (dis)equations, and prove its completeness. The ground part is dynamic in the sense that it continually changes. The algorithm saturates the non-ground equations using Superposition modulo the ground theory. We also have an Instantiation rule that matches the left hand side of non-ground (dis)equations with ground terms, creating new ground (dis)equations, which changes the ground theory. This algorithm can be used in quantified SMT problems, where the dynamic ground theory represents the evolving model. We develop an ordering to compare terms modulo a ground theory, which is used to orient non-ground equations. We prove properties of this ordering, using a weak form of monotonicity and subterm property. We finally present a set of inference rules for our ordering, which allows us to properly orient equations in theories of some finite data structures, such as a theory of finite lists with length and append.