The Visual Object Query Language (VOQL) recently proposed for object databases has been successful in visualizing path expressions and set-related conditions, and providing formal semantics. However, VOQL has several problems. Due to unrealistic assumptions, only set-related conditions can be represented in VOQL. Due to the lack of explicit language construct for the notion of variables, queries are often awkard and less intuitive. In this paper, we propose VOQL*, which extends VOQL to remove these drawbacks. We introduce the notion of visual variables and refine the syntax and semantics of VOQL based on visual variables. We carefully design the language constructs of VOQL* to reflect the syntax of OOPC, so that the constructs such as visual variables, visual elements, VOQL* simple terms, VOQL* structured terms, VOQL* basic formulas, VOQL* formulas, and VOQL* query expressions are hierarchically and inductively constructed as those of OOPC. Most important, we formally define the semantics of each language construct of VOQL* by induction using OOPC. Because of the well-defined syntax and semantics, queries in VOQL* are clear, concise, and intuitive. We also provide an effective procedure to translate queries in VOQL* into those in OOPC. We believe that VOQL* is the first visual query language with the well-defined syntax reflecting the syntactic structure of logic and semantics formally defined by induction.