## Generalized Topological Semantics for First-Order Modal Logic (2010)

by
Kohei Kishida

by
Kohei Kishida

@MISC{Kishida10generalizedtopological,

author = {Kohei Kishida},

title = {Generalized Topological Semantics for First-Order Modal Logic },

year = {2010}

}

This dissertation provides a new semantics for first-order modal logic. It is philosophically motivated by the epistemic reading of modal operators and, in particular, three desiderata in the analysis of epistemic modalities. (i) The semantic modelling of epistemic modalities, in particular verifiability and falsifiability, cannot be properly achieved by Kripke’s relational notion of accessibility. It requires instead a more general, topological notion of accessibility. (ii) Also, the epistemic reading of modal operators seems to require that we combine modal logic with fully classical first-order logic. For this purpose, however, Kripke’s semantics for quantified modal logic is inadequate; its logic is free logic as opposed to classical logic. (iii) More importantly, Kripke’s semantics comes with a restriction that is too strong to let us semantically express, for instance, that the identity of Hesperus and Phosphorus, even if metaphysically necessary, can still be a matter of epistemic discovery. To provide a semantics that accommodates the three desiderata, I show, on the one hand, how the desideratum (i) can be achieved with topological semantics, and more generally neighborhood semantics, for propositional modal logic. On the other hand, to achieve (ii) and (iii), it turns out

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