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A Content Semantics for Quantified Relevant Logics. I

Ross T. Brady
Studia Logica: An International Journal for Symbolic Logic
Vol. 47, No. 2 (1988), pp. 111-127
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015362
Page Count: 17
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A Content Semantics for Quantified Relevant Logics. I
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Abstract

We present an algebraic-style of semantics, which we call a "content semantics", for quantified relevant logics based on the weak system BBQ. We show soundness and completeness for all quantificational logics extending BBQ and also treat reduced modelling for all systems containing $BB^{d}Q$. The key idea of content semantics is that true entailments A → B are represented under interpretation I as content containments, i.e. $I(A)\leq I(B)$ (or, the content of A contains that of B). This is opposed to the truth-functional way which represents true entailments as truth-preservations over all set-ups (or worlds), i.e. (∀a ∈ K) (if I(A, a)= T then I(B, a) = T).

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