Enumeration Problems Related to Ground Horn Theories
  We investigate the enumeration of varieties of boolean theories related to Horn clauses. We describe a number of combinatorial equivalences among different characterizations and calculate the number of different theories in $n$ variables for slightly different characterizations. The method of counting is via counting models using a satisfiability checker. 
Nachum Dershowitz, Mitchell A. Harris, and Guan-Shieng Huang