Fischer-Ladner Closure for Many-Sorted Modal Logic with Application for Operational Semantics

In prior work we have developed a many-sorted polyadic modal logic. Progressively adding different operations and binders, we expressed operational semantics, thus enabling us to certify execution. In this paper we prove standard completeness for a many-sorted hybrid modal logic with satisfaction operators and PDL-inspired axioms. In order to do this, we define the Fischer-Ladner closure for our particular system and we prove a variant of the small model property.