# Dynamic Term-Modal Logics for First-Order Epistemic Planning

## TL;DR

This paper introduces a first-order dynamic epistemic logic framework that combines higher-order reasoning with lifted representations, enabling compact multi-agent epistemic planning with formal semantics and completeness results.

## Contribution

It develops a novel first-order dynamic epistemic logic with action models and schemas, integrating DEL's reasoning capabilities with first-order expressiveness for planning.

## Key findings

- Defines a first-order epistemic language with possible-worlds semantics
- Introduces first-order action models and product updates for dynamics
- Establishes completeness and decidability results for the framework

## Abstract

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.