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A Second-Order Relevance Logic with Modality

James B. Freeman and Charles B. Daniels
Studia Logica: An International Journal for Symbolic Logic
Vol. 38, No. 2 (1979), pp. 113-135
Published by: Springer
Stable URL: http://www.jstor.org/stable/20014936
Page Count: 23
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A Second-Order Relevance Logic with Modality
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Abstract

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts of the semantic notions of a possible world and the Routley-Meyer * operator.

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