Bringing closure to theory combination properties
This work addresses a theoretical problem for researchers in automated reasoning and satisfiability modulo theories (SMT), specifically concerning the properties of combined theories.
This paper investigates the closure of stable infiniteness, gentleness, and shininess (or strong politeness) under intersection and combinability. The authors systematically compute all possible intersections and then determine the maximal set of theories that can be combined with each resulting intersection, iterating until no new sets are found.
We consider the closure of three classical combination properties, namely, stable infiniteness, gentleness and shininess (or, equivalently for decidable theories, strong politeness), under intersection and combinability. We compute every possible intersection, and then compute the maximal set of theories that can be combined with each resulting intersection. We iterate this process until no new sets are identified. How many properties will we end up with?