Introducing LoCo, a Logic for Configuration Problems

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.

💡 Research Summary

The paper introduces LoCo, a new logic‑based framework designed to model configuration problems in a declarative and intuitive manner while guaranteeing that every configuration contains only finitely many components. Traditional knowledge‑representation approaches for configuration either require explicit bounds on the number of generated components or embed detailed algorithmic knowledge into the model, which hampers scalability and usability. LoCo addresses these issues by extending a fragment of classical first‑order logic (FO) with existential counting quantifiers (∃⁽ˡ,ᵘ⁾), which allow the specification of lower and upper bounds on the number of objects satisfying a given predicate.

A component of kind Cᵢ is represented as an n‑ary predicate Component(id, ~x), where id is a unique identifier and ~x is a vector of attribute values. Types are introduced for identifiers and attributes, and a standard many‑sorted‑to‑single‑sorted reduction is employed: each type gets a unary predicate (e.g., ID) and domain‑partitioning axioms enforce disjointness.

Connections between components are captured by binary predicates C₁₂C₂ and C₂₂C₁. For each direction a rule of the form

 ∀ id₁, ~x