A general framework for dynamic epistemic logic: towards canonical correspondences

On Inverse Operators in Dynamic Epistemic Logic

“…Similar results not involving inverse operators are shown in[6,15,16,23,24] 4. A previous work[16] studies this construction in more general settings without the assumption of the functionality of MTSs in the ordinary language without inverse operators.…”

“…Secondly, decidability of PAL + and EA + should be addressed. Thirdly, for the generalised notion of MTS proposed in [16], whose model transitions t α are not necessarily functional, we shall study its categorical reformulation and whether analogous results regarding inverse operators given in this paper hold. Lastly, the MTS construction in Sect.…”

“…Categorical semantics of DEL in [9,13,14] does not have such indexing systems. On the other hand, the first author extends index update functions (t α component of MTS) to relations in [16]. This extension is beyond the categorical framework in Sect.…”

“…Dynamic Epistemic Logic (DEL) is a branch of modal logic for reasoning about knowledge changes or belief revisions caused by communication [10,16]. Up until today, many DELs for various kinds of actions of communications have been proposed and studied: Public Announcement Logic (PAL) [17], Epistemic Action Logic (EA) [3], Preference Upgrade [7], etc.…”

“…This notion is called a functional MTS in[16] since any t α in an MTS (I, (Mi)i∈I , T ) with T = ((t α )α∈A, (T α i )α∈A,i∈I ) is a function. Inverse operators in the more general settings where each t α is a relation is a part of our future work.…”