Viktor Kuncak and Martin Rinard. On role logic. Technical Report 925, MIT CSAIL, 2003.

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates. The unrestricted version of role logic has the expressive power of first-order logic with transitive closure. Using a syntactic restriction on role logic formulas, we identify a natural fragment RL² of role logic. We show that the RL² fragment has the same expressive power as two-variable logic with counting C², and is therefore decidable. We present a translation of an imperative language into the decidable fragment RL², which allows compositional verification of programs that manipulate relational structures. In addition, we show how RL² encodes boolean shape analysis constraints and an expressive description logic.

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