Forgetting Formulas and Signature Elements in Epistemic States

TL;DR

This paper unifies Delgrande's syntactic forgetting with marginalisation in epistemic states, showing marginalisation as a specific, informative forgetting operator, and highlights fundamental differences between forgetting syntax and belief contraction.

Contribution

It extends Delgrande's axioms of forgetting to epistemic states and demonstrates that marginalisation is the most specific operator satisfying these axioms.

Findings

Marginalisation can be viewed as an extension of Delgrande's forgetting to epistemic states.

Forgetting formulas via Delgrande's approach leads to trivial methods.

Forgetting syntax elements is fundamentally different from belief contraction.

Abstract

Delgrande's knowledge level account of forgetting provides a general approach to forgetting syntax elements from sets of formulas with links to many other forgetting operations, in particular, to Boole's variable elimination. On the other hand, marginalisation of epistemic states is a specific approach to actively reduce signatures in more complex semantic frameworks, also aiming at forgetting atoms that is very well known from probability theory. In this paper, we bring these two perspectives of forgetting together by showing that marginalisation can be considered as an extension of Delgrande's approach to the level of epistemic states. More precisely, we generalize Delgrande's axioms of forgetting to forgetting in epistemic states, and show that marginalisation is the most specific and informative forgetting operator that satisfies these axioms. Moreover, we elaborate suitable phrasings of Delgrande's concept of forgetting for formulas by transferring the basic ideas of the axioms to forgetting formulas from epistemic states. However, here we show that this results in trivial approaches to forgetting formulas. This finding supports the claim that forgetting syntax elements is essentially different from belief contraction, as e.g. axiomatized in the AGM belief change framework.