Dynamic Term-Modal Logics for First-Order Epistemic Planning
This work addresses the need for more expressive planning frameworks in AI, particularly for multi-agent systems involving higher-order reasoning, though it is incremental as it builds on existing dynamic epistemic logic.
The paper tackles the problem of integrating first-order logic with dynamic epistemic logic to enable compact, lifted representations for multi-agent epistemic planning, resulting in a formalism that supports epistemic action schemas and demonstrates decidability for finite agents along with completeness results.
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists x\mathsf{blocks\_door}(x)$. In contrast, several recent epistemic planning frameworks are built on propositional epistemic logic. The epistemic language is useful to describe planning problems involving higher-order reasoning or epistemic goals such as $K_{a}\neg\mathsf{problem}$. This paper develops a first-order version of Dynamic Epistemic Logic (DEL). In this framework, for example, $\exists xK_{x}\exists y\mathsf{blocks\_door}(y)$ is a formula. The formalism combines the strengths of DEL (higher-order reasoning) with those of first-order logic (lifted representation) to model multi-agent epistemic planning. The paper introduces an epistemic language with a possible-worlds semantics, followed by novel dynamics given by first-order action models and their execution via product updates. Taking advantage of the first-order machinery, epistemic action schemas are defined to provide compact, problem-independent domain descriptions, in the spirit of PDDL. Concerning metatheory, the paper defines axiomatic normal term-modal logics, shows a Canonical Model Theorem-like result which allows establishing completeness through frame characterization formulas, shows decidability for the finite agent case, and shows a general completeness result for the dynamic extension by reduction axioms.