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Generalized Topological Semantics for First-Order Modal Logic1

Summary: Generalized Topological Semantics for
First-Order Modal Logic1
Kohei Kishida
Draft of November 14, 2010.
Draft of November 14, 2010
Abstract. This dissertation provides a new semantics for first-order modal logic. It is philosophi-
cally 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 quanti-
fied 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 se-
mantically express, for instance, that the identity of Hesperus and Phosphorus, even if meta-
physically 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 se-


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics