Giacomo Bonanno, Supposing and learning: a unified framework for belief revision
Abstract.
Consider two possible scenarios for belief revision. Initially the
agent either believes that A is not the case (that is, believes not-A)
or suspends belief about A. In one scenario she receives reliable
information that, as a matter of fact, A is the case; call this
scenario "learning that A". In the other scenario she reasons about
what she believes would be the case if A were the case; call this
scenario "supposing that A". We argue that there are important
differences between the two scenarios. It was shown in
Bonanno G. Artificial Intelligence 339 (2025)
that it is possible to view the AGM theory of belief revision as a
theory of hypothetical, or suppositional, reasoning, rather than a
theory of actual belief change in response to new information. By
making an addition to the Kripke-Lewis semantics considered
in
Bonanno G. Artificial Intelligence 339 (2025),
we (1) provide a unified framework for the analysis of both
suppositional beliefs and information-driven belief change, (2) argue
that some of the AGM axioms are not appropriate for the latter and (3)
provide a list of axioms that seem appropriate for belief change in
response to new information..
Giacomo Bonanno, The logic of KM belief update is contained in the logic of AGM belief revision
Abstract.
For each axiom of KM belief update we provide a corresponding axiom in a
modal logic containing three modal operators: a unimodal belief
operator $B$, a bimodal conditional operator $>$ and the unimodal
necessity operator $\square$. We then compare the resulting logic to the
similar logic obtained from converting the AGM axioms of belief
revision into modal axioms and show that the latter contains the former.
Denoting the latter by L_{AGM} and the former by L_{KM} we show that
every axiom of L_{KM} is a theorem of L_{AGM} . Thus AGM belief revision
can be seen as a special case of KM belief update. For the strong
version of KM belief update we show that the difference between L_{KM}
and L_{AGM} can be narrowed down to a single axiom, which deals
exclusively with unsurprising information, that is, with formulas that
were not initially disbelieved.
