Applications of game theory to threshold logic

Recently,Owen demonstrated an isomorphism between characteristic function games and pseudo-Boolean functions. When a game is interpreted as a function on a lattice, then properties of pseudo-Boolean inequalities can be related to partitions of the lattice. The isomorphism also has important implications for threshold logic. In particular, by using a special reflection map, unate switching functions can be studied via monotone simple games. We can show that every unate switching function can be written as the join threshold functions. Also, using the ideas ofCharnes, Kortanek andKeene, we can give several ways to calculate approximate threshold inequalities for unate switching functions.