Non-determined game logic is the logic of two player board games where the game may end in a draw: unlike the case with determined games, a loss of one player does not necessarily constitute of a win of the other player. A calculus for non-determined game logic is given in [4] and shown to be complete. The calculus adds a new rule for the treatment of greatest fixpoints, and a new unfolding axi...

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it m...

We present our research on defining a correct semantics for forward chaining production systems (PS) programs. A correct semantics must ensure that the execution of the program is deterministic and that it will terminate. We define a class of function-free stratified PS programs, and develop a fixpoint semantics and a declarative semantics for these programs. A stratified PS program comprises a...

This paper contributes to a theory of the behaviour of “finite-state” systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if...

The nested model is an extension of the traditional, “flat” relational model in which relations can also have relationvalued entries. Its “default” query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, “flat” relational algebra, and thus can only express a small fraction of the polynomial-time queries. Therefore, it was ...

The μ-calculus model-checking problem has been of great interest in the context of concurrent programs. Beyond the need to use symbolic methods in order to cope with the state-explosion problem, which is acute in concurrent settings, several concurrency related problems are naturally solved by evaluation of μ-calculus formulas. The complexity of a naive algorithm for model checking a μ-calculus...

AsmL is a novel executable specification language based on the theory of Abstract State Machines (ASMs). It represents one of the most powerful practical engines to write and execute ASMs. In this report, we present a proven complete small-step trace-based operational semantics of the main parts of AsmL. Such a semantics provides precise and non ambiguous definitions of AsmL. It is very useful ...