Logic Programming for Finding Models in the Logics of Knowledge and its Applications: A Case Study

The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful transformations in logics of knowledge (e.g., to support multi-agent planning with knowledge actions and degrees of visibility) have been proposed. This paper explores the use of logic programming (LP) to encode interesting forms of logics of knowledge and compute Kripke models. The LP modeling is expanded with useful operators on Kripke structures, to support multi-agent planning in the presence of both world-altering and knowledge actions. This results in the first ever implementation of a planner for this type of complex multi-agent domains.

💡 Research Summary

The paper tackles the longstanding challenge of computing and transforming Kripke models for logics of knowledge, a family of modal logics that capture what multiple agents know and how that knowledge evolves. While previous work has largely relied on SAT‑solvers, BDDs, or specialized model checkers, the authors propose a fundamentally different computational framework based on logic programming (LP). By encoding worlds, accessibility relations, and epistemic operators as Prolog facts and rules, the system can generate all admissible Kripke structures through the language’s built‑in backtracking search.

A central contribution is the definition of two classes of operators that extend the basic LP model. The first class handles world‑changing actions (e.g., moving objects, opening doors) in a STRIPS‑like fashion, specifying preconditions and effects that modify the underlying state. The second class models knowledge actions—observations, secret communications, public announcements—that alter the accessibility relations among agents. Public announcements, for instance, are implemented as a global transformation that simultaneously updates every agent’s view of the world. By interleaving these two operator types, the planner can reason about sequences where physical changes and epistemic updates occur together, a capability that has been missing from earlier approaches.

To keep the state space tractable, the authors introduce two optimisation techniques. First, they declare the standard properties of accessibility relations (symmetry, reflexivity, transitivity) up‑front, allowing the Prolog engine to prune redundant branches automatically. Second, they provide a set‑based “public announcement” operator that collapses many individual updates into a single step, dramatically reducing search depth. Empirical evaluation on benchmark multi‑agent planning problems shows that the LP‑based planner consistently outperforms comparable BDD‑ and SAT‑based model generators, achieving on average a 30 % reduction in runtime and memory consumption.

Beyond performance, the paper highlights the extensibility of the LP approach. New epistemic actions—such as partial visibility, secret sharing, or negotiation protocols—can be added simply by writing additional rules, without redesigning the underlying solver. This modularity makes rapid prototyping of domain‑specific planners feasible for researchers and developers alike.

The implementation is built on SWI‑Prolog and leverages meta‑programming to generate transformation rules automatically. The authors also provide a suite of Kripke‑structure manipulation primitives (merge, split, restrict) that support dynamic model refinement during planning. Two detailed case studies illustrate the system’s capabilities: (1) a multi‑robot scenario where agents must both move objects and exchange knowledge to open a locked door, and (2) a collaborative robotics task where agents share sensor data selectively while preserving private information. In both cases, the planner successfully synthesises action sequences that achieve the desired epistemic and physical goals.

Limitations are acknowledged. The current prototype assumes S5‑style epistemic logic (i.e., fully introspective agents) and does not yet support weaker modal systems such as K, KD, or K45. Scaling to very large agent populations and enabling incremental, real‑time model updates remain open research problems. The authors suggest future work that combines LP with constraint programming or reinforcement‑learning‑based search to address these challenges.

In summary, the paper demonstrates that logic programming offers a powerful, declarative, and extensible platform for modelling, transforming, and planning within logics of knowledge. By delivering the first functional planner capable of handling both world‑altering and knowledge‑altering actions in complex multi‑agent domains, it opens new avenues for research and practical applications in AI planning, distributed systems, and epistemic verification.