In this paper we introduce the idea of using games as a driving metaphor for design tools which support designers working in UML.

Abstract. We extend the open answer set semantics for programs with generalized literals. Such extended programs (EPs) have interesting properties, e.g. the ability to express infinity axioms- EPs that have but infinite answer sets. However, reasoning under the open answer set semantics, in particular satisfiability checking of a predicate w.r.t. a program, is already undecidable for programs without generalized literals. In order to regain decidability, we restrict the syntax of EPs such that both rules and generalized literals are guarded. Viaa translation to guarded fixed point logic (µGF), in which satisfiability checking is 2-EXPTIME-complete, we deduce 2-EXPTIME-completeness of satisfiability checking in such guarded EPs (GEPs). Bound GEPs are restricted GEPs with EXPTIME-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog LITE programs to GEPs, establishing equivalence of GEPs under an open answer set semantics, alternation-free µGF, and Datalog LITE. Finally, we discuss ω-restricted logic programs under an open answer set semantics. 1

Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are (1) MLFP can describe graph properties beyond any fixed level of the monadic secondorder quantifier alternation hierarchy. (2) On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. (3) Settling the question whether addition-invariant MLFP? = addition-invariant MSO on finite strings or, equivalently, settling the question whether MLFP? = MSO on finite strings with addition would solve open problems in complexity theory: “= ” would imply that PH = PTIME whereas “�= ” would imply that DLIN � = LINH. Apart from this we give a self-contained proof of the previously known result that MLFP is strictly less expressive than MSO on the class of finite graphs.