# Progression of Decomposed Local-Effect Action Theories

## TL;DR

This paper investigates how decomposability and inseparability of logical theories are affected by progression in the situation calculus, providing conditions for their preservation or loss after theory updates due to actions.

## Contribution

It studies the preservation of decomposability and inseparability properties under progression and forgetting in local-effect basic action theories, bridging modularity and reasoning about actions.

## Key findings

- Identifies conditions when properties are preserved during progression.
- Demonstrates cases where properties are lost after theory updates.
- Provides negative examples illustrating boundaries of property preservation.

## Abstract

In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly-related or independent components. However, a theory may represent knowledge that is subject to change, as a result of executing actions that have effects on some of the initial properties mentioned in the theory. Having once computed a decomposition of a theory, it is advantageous to know whether a decomposition has to be computed again in the newly-changed theory (obtained from taking into account changes resulting from execution of an action). In the paper, we address this problem in the scope of the situation calculus, where a change of an initial theory is related to the notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those properties, which are subject to change, and computing new values for them. We consider decomposability and inseparability, two component properties known from the literature, and contribute by 1) studying the conditions when these properties are preserved and 2) when they are lost wrt progression and the related operation of forgetting. To show the latter, we demonstrate the boundaries using a number of negative examples. To show the former, we identify cases when these properties are preserved under forgetting and progression of initial theories in local-effect basic action theories of the situation calculus. Our paper contributes to bridging two different communities in Knowledge Representation, namely research on modularity and research on reasoning about actions.