Public Announcement Logic (PAL) models knowledge update as world elimination, with the well‑known property that truthful announcements commute: learning p then q yields the same epistemic state as learning q then p. This commutativity is typically treated as a harmless algebraic convenience. I argue that it encodes a substantive philosophical assumption: that epistemic justification is independent of the order in which information is acquired. To make this hidden commitment visible, I introduce …
Read morePublic Announcement Logic (PAL) models knowledge update as world elimination, with the well‑known property that truthful announcements commute: learning p then q yields the same epistemic state as learning q then p. This commutativity is typically treated as a harmless algebraic convenience. I argue that it encodes a substantive philosophical assumption: that epistemic justification is independent of the order in which information is acquired. To make this hidden commitment visible, I introduce a minimal trace‑augmented semantics that retains a record of past announcements and adds a single memory operator Prev(φ). Using a simple three‑world example, I show that the sequences p;q and q;p are indistinguishable in standard PAL but become distinguishable in the extended language: they differ in their evaluation of Prev formulas. This yields a precise expressive limitation: PAL identifies epistemic states solely by their set of possible worlds, thereby quotienting away all information about epistemic history. The result is not a rejection of PAL but a clarification of what it assumes. If the order of evidence and justificational structure matter for epistemology, then commutative update semantics is not a neutral tool but a representational choice with substantive philosophical consequences.
