It　is　demonstrated　that　the　logic　tool　used　in　agent　formalized　depiction　should　be　the　mixed　modal　logic　which　has　both　normal　and　non-normal　modal　operators.　Then　a　logic　system　A-BI　is　built　for　Agent-BDI　logic　and　its　semantics　and　axiom　system　are　discussed.　Especially　for　non-normal　modal　operators　a　new　semantic　interpretation　based　on　Kripke＇s　normal　possible　worlds　is　presented.　It　is　proved　that　A-BI　logic　system　is　sound　and　complete.　A-BI　logic　appropriately　depicts　the　essence　and　relation　of　belief　and　intention,　and　can　be　used　as　logic　tool　in　formalized　research　on　agent.