Formal　frameworks　for　the　specification　of　rational　agents　are　commonly　based　on　logic　of　belief,　desire　and　intention.　In　order　to　eliminate　the　problems　with　existing　logic　of　belief,　desire　and　intention,　and　to　provide　a　proper　semantic　representation　for　non-normal　modal　operator,　the　problems　with　existing　logic　of　belief,　desire　and　intention　are　addressed,　the　true-false　subset　semantics,　which　is　developed　by　the　authors,　and　its　application　in　the　formalization　of　agent　are　introduced.　The　proposed　framework　invalidates　the　problematic　properties　of　intention,　and　by　imposing　certain　constraints　on　the　algebraic　structure　of　the　models,　it　is　showed　that　many　desirable　properties　can　be　obtained.　Finally　the　true-false　subset　semantics　is　analyzed.　Thus　the　true-false　subset　semantics　provides　a　proper　semantic　representation　for　non-normal　modal　operator.　It　is　an　important　development　of　classical　possible　worlds　semantics　for　normal　modal　operators,　and　is　proved　to　be　a　powerful　tool　for　the　logical　specification　of　rational　agent　behavior.　It　can　be　applied　to　establish　a　new　proper　agent　logic　system.