## Combining Theories with Shared Set Operations

Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theorem and apply it to show the decidability of the satisfiability problem for a class of formulas obtained by applying propositional connectives to formulas belonging to: 1) Boolean Algebra with Presburger Arithmetic (with quantifiers over sets and integers), 2) weak monadic second-order logic over trees (with monadic second-order quantifiers), 3) two-variable logic with counting quantifiers (ranging over elements), 4) the EPR class of first-order logic with equality (with exists*forall* quantifier prefix), and 5) the quantifier-free logic of multisets with cardinality constraints.

Editor(s):
Ghilardi, Silvio
Sebastiani, Roberto
Published in:
Proceedings of the 7th International Symposium on Frontiers of Combining Systems, 366-382
Presented at:
7th International Symposium on Frontiers of Combining Systems, Trento, Italy, September 16-18, 2009
Year:
2009
Publisher:
Springer
Keywords:
Laboratories: