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Junior Analysis Seminar: Making Modal Logic Continuous

Author: Lona

Speaker: Caleb Camrud

Abstract: Modal language is used to model possibility, obligation, access to knowledge, and more. Logics of these modalities were then developed to reflect how we reason using modal language. But some modalities seem to exist in a continuum, rather than being discretely ordered. For a classic metaphysical example, it seems that the possible world in which I became a lawyer is more similar to the actual world than the possible world in which I am a frog. Indeed there intuitively seems to be an entire continuum of possible worlds “between” our actual world and the world in which I am a frog. As such, Dr. Ranpal Dosanjh (Iowa State University, Department of Philosophy) and I developed a method for making modal logic continuous. In this talk, I will present the syntax and semantics of basic modal logic, and discuss our method for constructing continuous modal logic.