Effective AGM Belief Contraction: A Journey beyond the Finitary Realm (Technical Report)
- URL: http://arxiv.org/abs/2409.09171v2
- Date: Mon, 04 Aug 2025 20:12:30 GMT
- Title: Effective AGM Belief Contraction: A Journey beyond the Finitary Realm (Technical Report)
- Abstract summary: We investigate the computability of AGM contraction on non-finitary logics.<n>We show that there are infinitely many uncomputable AGM contraction functions in such logics.<n>We propose new approaches to controlling computability beyond the finitary realm.
- Score: 1.6590638305972631
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary logics, and show an intriguing negative result: there are infinitely many uncomputable AGM contraction functions in such logics. Drastically, we also show that the current de facto standard strategies to control computability, which rely on restricting the space of epistemic states, fail: uncomputability remains in all non-finitary cases. Motivated by this disruptive result, we propose new approaches to controlling computability beyond the finitary realm. Using Linear Temporal Logic (LTL) as a case study, we identify an infinite class of fully-rational AGM contraction functions that are computable by design. We use B\"uchi automata to construct such functions, and to represent and reason about LTL beliefs.
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