Lattice Annotated Temporal (LAT) Logic for Non-Markovian Reasoning
This paper addresses efficiency and expressiveness bottlenecks in existing logical systems for non-Markovian temporal reasoning and open-world semantic modeling. We propose Lattice-Annotated Temporal Logic (LAT Logic), a novel framework that integrates generalized lattice annotation into temporal logic programming. By leveraging an underlying lattice structure, LAT Logic explicitly supports the open-world assumption and enables efficient instantiation over infinite domains—achieving, for the first time, a unified formalism for non-Markovian modeling and logic programming. Technically, it incorporates Skolemization, modular implementation, and seamless integration with reinforcement learning (RL) environments. Experiments demonstrate that LAT Logic accelerates logical inference by up to three orders of magnitude and reduces memory consumption by five orders of magnitude. It matches or surpasses state-of-the-art methods on multi-agent simulation and knowledge graph reasoning tasks. In RL settings, simulation throughput increases threefold and agent win rates improve by 26%.