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A denotational semantics for a Lewis-style modal system close to S1 | | Steffen Lewitzka
; | | Date: |
25 Apr 2013 | | Abstract: | While possible worlds semantics provides a natural framework for normal modal
logics, there is no such intuitive semantics for modal system S1 designed by C.
I. Lewis as a logic of strict implication. In this paper, we interpret strict
equivalence
$square(varphi
ightarrowpsi)wedgesquare(psi
ightarrowvarphi)$ as
propositional identity $varphiequivpsi$ (read: "$varphi$ and $psi$ denote
the same proposition") and extend S1 by an inference rule which is a natural
generalization of the rule of Substitutions of Proved Strict Equivalents. The
resulting modal system is only slightly stronger than S1 and satisfies the
principles of non-Fregean logic. This enables us to develop an intuitive,
non-Fregean denotational semantics for which the system is sound and complete. | | Source: | arXiv, 1304.6983 | | Services: | Forum | Review | PDF | Favorites | |
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