Intentions,　a　crucial　part　of　the　mental　state　of　an　agent,　play　an　important　role　in　determining　the　behavior　of　rational　agents.　In　order　to　eliminate　the　flaws　with　existing　logic　of　intention,　in　this　paper,　we　address　the　requests　for　intention　semantics　on　formal　frameworks　of　rational　agents　and　the　problems　with　existing　logic　of　intention,　put　forward　a　novel　semantics　for　intention,　called　the　multi-subset　possible　world　semantics,　and　its　application　in　the　formalization　of　intention　for　agent.　The　multi-subset　possible　world　semantics　use　three　subsets　to　describe　intention.　It　not　only　avoids　the　logical　omniscience　problem　and　other　related　problems　(such　as　side-effect　problem,　and　etc)　but　also　overcomes　the　shortcomings　of　the　true-false　subset　semantics　and　twin-subset　semantics.　Compared　with　Konolige　and　Pollack＇s　model　of　intention,　this　semantics　model　doesn＇t　lose　the　reasoning　ability　of　non-equivalent　intention,　and　what＇s　more,　it　is　simpler,　more　natural　and　satisfies　the　K　axiom　and　the　Joint　Consistency.　Our　framework　invalidates　the　problematic　properties　with　existing　logic　of　intention.　And　by　imposing　certain　constraints　on　the　algebraic　structure　of　the　models,　many　desirable　properties　can　be　obtained.　At　last　we　make　an　analysis　for　the　multi-subset　possible　world　semantics.　Actually　the　multi-subset　possible　world　semantics　provides　a　new　method　for　semantic　representation　of　non-normal　modal　operators.　It　can　be　used　in　establishing　new　proper　agent＇s　logic　systems.