Rasmus K. Rendsvig

Gaia Belardinelli, Rasmus K. Rendsvig

The literature on awareness modeling includes both syntax-free and syntax-based frameworks. Heifetz, Meier \& Schipper (HMS) propose a lattice model of awareness that is syntax-free. While their lattice approach is elegant and intuitive, it precludes the simple option of relying on formal language to induce lattices, and does not explicitly distinguish uncertainty from unawareness. Contra this, the most prominent syntax-based solution, the Fagin-Halpern (FH) model, accounts for this distinction and offers a simple representation of awareness, but lacks the intuitiveness of the lattice structure. Here, we combine these two approaches by providing a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show our model equivalent to both HMS and FH models by defining transformations between them which preserve satisfaction of formulas of a language for explicit knowledge, and obtain completeness through our and HMS' results. Lastly, we prove that the Kripke lattice model can be shown equivalent to the FH model (when awareness is propositionally determined) also with respect to the language of the Logic of General Awareness, for which the FH model where originally proposed.

Gaia Belardinelli, Rasmus K. Rendsvig

Where information grows abundant, attention becomes a scarce resource. As a result, agents must plan wisely how to allocate their attention in order to achieve epistemic efficiency. Here, we present a framework for multi-agent epistemic planning with attention, based on Dynamic Epistemic Logic (DEL, a powerful formalism for epistemic planning). We identify the framework as a fragment of standard DEL, and consider its plan existence problem. While in the general case undecidable, we show that when attention is required for learning, all instances of the problem are decidable.

Andrés Occhipinti Liberman, Andreas Achen, Rasmus Kræmmer Rendsvig

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.

Dominik Klein, Rasmus K. Rendsvig

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.