On interpolants and variable assignments

Craig interpolants are widely used in program verification as a means of abstraction. In this paper, we (i) introduce Partial Variable Assignment Interpolants (PVAIs) as a generalization of Craig interpolants. A variable assignment focuses computed interpolants by restricting the set of clauses taken into account during interpolation. PVAIs can be for example employed in the context of DAG interpolation, in order to prevent unwanted out-of-scope variables to appear in interpolants. Furthermore, we (ii) present a way to compute PVAIs for propositional logic based on an extension of the Labeled Interpolation Systems, and (iii) analyze the strength of computed interpolants and prove the conditions under which they have the path interpolation property.