Description logics for shape analysis

Verification of programs requires reasoning about sets of program states. In case of programs manipulating pointers, program states are pointer graphs. Verification of such programs involves reasoning about unbounded sets of graphs. Three-valued shape analysis (Sagiv et. al.) is an approach based on explicit manipulation of 3-valued shape graphs, which abstract sets of pointer graphs. Other approaches use symbolic representations, e.g., by describing (sets of) graphs as logical formulas. Unfortunately, many resulting logics are either undecidable or cannot express crucial properties like reachability and separation. In this paper, we investigate an alternative approach. We study well-known description logics as a framework for symbolic shape analysis. We propose a predicate abstraction based shape analysis, parameterized by description logics to represent the abstraction predicates. Depending on the particular logic chosen sharing, reachability and separation in pointer data structures are expressible.