I'm planning to write a paper about the possibility of describing modal logic and the multiple world aspect of it with techniques of automata theory. To not duplicate my work does anyone have more explicit links to done research in this area. My university doesn't seem to show anything specific in their database. Thanks beforehand.
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- $\begingroup$ Googling modal logic and automata gives several hits. $\endgroup$Benjamin Steinberg– Benjamin Steinberg2016-10-29 17:54:40 +00:00Commented Oct 29, 2016 at 17:54
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2 What sources are you using for modal logic? What aspects of modal logic are you considering?
In for instance, the book: Tools and Techniques in Modal Logic, by Kracht, the section on Dynamic Logic includes a brief discussion of finite automata as it is relevant to that logic. Another perhaps more useful source to examine would be `Epistemic Logic for AI and Computer Science, Number 41 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1995. That looks at computer science ideas for epistemic logics and hence does treat certain things that may be of relevance to your work.
Without your being a bit more detailed on the type of results that you are considering, I cannot be sure if the material in these books provides an answer to your question. (I understand you may be reluctant to be too explicit if it is still `work in progress'.)
Some time ago I looked at using various ideas not that far from automata theory to model the modal logics (S5n in particular) that were being used in the theory of multiagent systems. Perhaps there might be some useful way of applying automata theory in that context as well.
- $\begingroup$ Actually your provided examples look very interesting I will definitely take a close look to those. It is indeed 'work in progress'. My question was by that more about if someone knows if deeper research has been done in the field of connecting these two areas. $\endgroup$blub– blub2016-10-29 14:01:18 +00:00Commented Oct 29, 2016 at 14:01
- $\begingroup$ I have not checked the second text for references to automata as such, but it is a fun read and should provide you with some good motivational points on which to fine tune your ideas. $\endgroup$Tim Porter– Tim Porter2016-10-29 15:27:26 +00:00Commented Oct 29, 2016 at 15:27