||On Generalized Records and Spatial Conjunction in Role Logic
|LCS Document Number:
|We have previously introduced role logic as a notation for
describing properties of relational structures in shape
analysis, databases and knowledge bases. A natural fragment
of role logic corresponds to two-variable logic with
counting and is therefore decidable.
We show how to use role logic to describe open and closed
records, as well the dual of records, inverse records. We
observe that the spatial conjunction operation of separation
logic naturally models record concatenation. Moreover, we
show how to eliminate the spatial conjunction of formulas of
quantifier depth one in first-order logic with counting. As
a result, allowing spatial conjunction of formulas of
quantifier depth one preserves the decidability of
two-variable logic with counting. This result applies to
two-variable role logic fragment as well.
The resulting logic smoothly integrates type system and
predicate calculus notation and can be viewed as a natural
generalization of the notation for constraints arising in
role analysis and similar shape analysis approaches.
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