Automatic Decidability for Theories with Counting Operators

Elena Tushkanova (1, 2) , Christophe Ringeissen (1) , Alain Giorgetti (1, 2) , Olga Kouchnarenko (1, 2)

1 CASSIS - Combination of approaches to the security of infinite states systems
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

The notion of schematic paramodulation has been introduced to reason on properties of (standard) paramodulation. We present a schematic paramodulation calculus modulo a fragment of arithmetics, namely the theory of Integer Offsets. This new schematic calculus is used to prove the decidability of the satisfiability problem for some theories equipped with counting operators. We illustrate our theoretical contribution on theories representing extensions of classical data structures, e.g., lists and records.

Domaines: Logique en informatique [cs.LO]

Elena Tushkanova, Christophe Ringeissen, Alain Giorgetti, Olga Kouchnarenko. Automatic Decidability for Theories with Counting Operators. Automated Deduction: Decidability, Complexity, Tractability (workshop ADDCT), Jun 2013, Lake Placid, United States. ⟨hal-00920496⟩