  This work addresses the problem of long-horizon task planning with the Large
Language Model (LLM) in an open-world household environment. Existing works
fail to explicitly track key objects and attributes, leading to erroneous
decisions in long-horizon tasks, or rely on highly engineered state features
and feedback, which is not generalizable. We propose an open state
representation that provides continuous expansion and updating of object
attributes from the LLM's inherent capabilities for context understanding and
historical action reasoning. Our proposed representation maintains a
comprehensive record of an object's attributes and changes, enabling robust
retrospective summary of the sequence of actions leading to the current state.
This allows continuously updating world model to enhance context understanding
for decision-making in task planning. We validate our model through experiments
across simulated and real-world task planning scenarios, demonstrating
significant improvements over baseline methods in a variety of tasks requiring
long-horizon state tracking and reasoning. (Video\footnote{Video demonstration:
\url{https://youtu.be/QkN-8pxV3Mo}.})
