Gerda Janssens

Matthias van der Hallen, Sergey Paramonov, Michael Leuschel et al.

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining problem as an example of a higher order problem. In short, this problem asks us to find a graph that frequently occurs as a subgraph among a set of example graphs. We start from the problem's mathematical definition to solve it in three state-of-the-art specification systems. For IDP and ASP, which have no native support for higher order logic, we propose the use of encoding techniques such as the disjoint union technique and the saturation technique. ProB benefits from the higher order support for sets. We compare the performance of the three approaches to get an idea of the overhead of the higher order support. We propose higher-order language extensions for IDP-like specification languages and discuss what kind of solver support is needed. Native higher order shifts the burden of rewriting specifications using encoding techniques from the user to the solver itself.

Joachim Jansen, Jo Devriendt, Bart Bogaerts et al.

PC(ID) extends propositional logic with inductive definitions: rule sets under the well-founded semantics. Recently, a notion of relevance was introduced for this language. This notion determines the set of undecided literals that can still influence the satisfiability of a PC(ID) formula in a given partial assignment. The idea is that the PC(ID) solver can make decisions only on relevant literals without losing soundness and thus safely ignore irrelevant literals. One important insight that the relevance of a literal is completely determined by the current solver state. During search, the solver state changes have an effect on the relevance of literals. In this paper, we discuss an incremental, lightweight implementation of a relevance tracker module that can be added to and interact with an out-of-the-box SAT(ID) solver.

Ingmar Dasseville, Gerda Janssens

IDP is a knowledge base system based on first order logic. It is finding its way to a larger public but is still facing practical challenges. Adoption of new languages requires a newcomer-friendly way for users to interact with it. Both an online presence to try to convince potential users to download the system and offline availability to develop larger applications are essential. We developed an IDE which can serve both purposes through the use of web technology. It enables us to provide the user with a modern IDE with relatively little effort.