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Recently I read all kinds of work from logic scientists in which epistemic logic was the main topic. Where epistmic change refers to change in knowledge of some agent in a multi-agent system (in a non-changing world), ontic change refers to change in the factual world.

What I was wondering about is how one can add the dimension of time to an epistemic system (or possibly in a system in which the ontic changes included). For example to formalize things like:

  • After a certain point (in the future) A will know that p is the case (but up to then A does not know that p, while it was already the case)
  • A knows that after a certain point in the future, p will be the case (and she knows that until then, p is not the point.
  • B previously knew that p was the case, but now (because, maybe the facts in the world changed or A had a brain attack) does not know wheter p is true.

where A,B,q are agents and propositional formulas.

My main question is: what is the default paradigm/model/language/logical systems to express the sentences above? And how can one visualize it (for example by using (extended) Kripke-models?

  • This may be of interest to you : [en.wikipedia.org/wiki/Temporal_logic ] . Kripke is mentioned as having influenced its development. – Nick R Jun 21 '15 at 0:30
  • That is just temp. Logic. Im looking for systems in which epistemic and time Logic are combined.. – Applied mathematician Jun 21 '15 at 0:36
  • So just combine them. Temporal Kripke models and epistemic propositions combine nicely, you can even throw in degrees of belief. Academics separate these for clarity, but AI folks know that they just slide back together as largely independent factors. – jobermark Jun 21 '15 at 15:38
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What you are looking for is called dynamic epistemic logic, it was developed starting in late 1980s to represent changes in knowledge. Internet Encyclopedia of Philosophy gives a nice overview with many references: "The modal knowledge operators in epistemic logic are formally interpreted by employing binary accessibility relations in multi-agent Kripke models (relational structures), where these relations should be equivalence relations to respect the properties of knowledge. The operators for change of knowledge correspond to another sort of modality, more akin to a dynamic modality. A peculiarity of this dynamic modality is that it is interpreted by transforming the Kripke structures used to interpret knowledge, and not, at least not on first sight, by an accessibility relation given with a Kripke model".

Representation of factual ("ontic") change is even more recent, see Logics of Communication and Change by van Benthem, van Eijck and Kooi (2006):"We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events".

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