Symmetry Breaking for Distributed Multi-Context Systems

Heterogeneous nonmonotonic multi-context systems (MCS) permit different logics to be used in different contexts, and link them via bridge rules. We investigate the role of symmetry detection and symmetry breaking in such systems to eliminate symmetric parts of the search space and, thereby, simplify the evaluation process. We propose a distributed algorithm that takes a local stance, i.e., computes independently the partial symmetries of a context and, in order to construct potential symmetries of the whole, combines them with those partial symmetries returned by neighbouring contexts. We prove the correctness of our methods. We instantiate such symmetry detection and symmetry breaking in a multi-context system with contexts that use answer set programs, and demonstrate computational benefit on some recently proposed benchmarks.

💡 Research Summary

The paper addresses the problem of symmetry in heterogeneous, non‑monotonic Multi‑Context Systems (MCSs) and proposes a distributed framework for both detecting and breaking such symmetries. An MCS consists of several contexts, each possibly employing a different logic (the authors focus on Answer Set Programming, ASP), linked by bridge rules that import beliefs from other contexts. Symmetries arise when permutations of atoms leave the knowledge bases and bridge rules unchanged; these redundancies can cause evaluation algorithms to explore many equivalent states, dramatically inflating the search space.

The authors first formalize the notion of a symmetry of an MCS as a permutation of the global alphabet that preserves, for every context, its language, knowledge base, and bridge rules. They then introduce partial and local symmetries, which affect only a subset of contexts, and define a join operation that merges compatible partial symmetries into larger ones. Theorem 1 proves that any partial symmetry covering all contexts is a full symmetry, and that the join of two compatible partial symmetries yields a partial symmetry for the union of their contexts.

Building on these definitions, a distributed symmetry‑detection algorithm is presented. Each context independently constructs a coloured graph representing its ASP program and bridge‑rule atoms, then uses a graph‑automorphism tool (e.g., NAUTY, SAUCY) to compute a generating set of local symmetries. These generators are exchanged with neighbouring contexts; when two sets are compatible, the join operation produces a new partial symmetry that is propagated further. The process runs as background tasks within each context, requiring only asynchronous message passing, and converges to a set of candidate symmetries for the whole system without central coordination.

For symmetry breaking, the authors adapt the symmetry‑breaking constraints (SBCs) originally devised for SAT/ASP to the multi‑context setting. Each context generates SBCs that eliminate symmetric models locally, while also taking into account atoms imported via bridge rules. In ASP contexts the SBCs are encoded as additional rules, allowing existing ASP solvers to enforce them transparently.

Experimental evaluation uses recently proposed MCS benchmarks that model realistic scenarios such as database repair, data integration, and multi‑agent belief exchange. The benchmarks contain large symmetry groups (e.g., swapping of repair atoms). Results show that even breaking a subset of the generators yields substantial reductions in both runtime (often >30 % speed‑up) and memory consumption. Moreover, the distributed approach scales better than a naïve centralized symmetry detection, because each context handles only its own fragment of the problem.

The paper concludes that the combination of local symmetry detection, join‑based composition, and distributed SBC generation provides an effective, scalable method for handling symmetry in heterogeneous MCSs. Future work is suggested on extending the framework to other non‑monotonic logics, dynamic addition/removal of contexts, and integrated heuristics that balance detection cost against breaking benefit.