Introducing LoCo, a Logic for Configuration Problems

Abstract

In this paper we present the core of LoCo, a logic-based high-level representation language for expressing configuration problems. LoCo shall allow to model these problems in an intuitive and declarative way, the dynamic aspects of configuration notwithstanding. Our logic enforces that configurations contain only finitely many components and reasoning can be reduced to the task of model construction.

LoCo—A Logic for Configuration Problems

“…Observe that this is a stronger result than the one presented in [1]: Whenever the algorithm returns "no" the model can be made infinite by adding components that are not connected to other components.…”

“…The present work extends [1] as follows: We extend the language of LoCo by axiom types (6) and (7). Next we present a stronger version of Proposition 1 as well as complexity results related to enforcing finite configurations.…”

“…When l = u in the counting quantifier we can address each component instance and the respective attributes individually, abbreviated here as e.g. big [1] and big [2]. While the order of the instances is not defined there clearly exists a permutation such that the constraint is satisfied.…”

“…Next we present a stronger version of Proposition 1 as well as complexity results related to enforcing finite configurations. We show how integer programming can be used for bounds computation instead of the propagation algorithm presented in [1]. Finally we present a prototypical implementation.…”

“…This work is closely related to dynamic and composite CSP, and hence does not come with support for describing component ports and connections. In [1] LoCo has been introduced. LoCo is also a fragment of first order logic, allows to describe arbitrary component topologies and implicitly bounds the number of components needed through the axioms and a number of explicitly bounded components.…”