Abstract
A (partial) valuation for a language S on a set T of reference points is a (partial) function v: T × S → {0,1}. A (partial) frame interpretation for S is a couple (f, H), where f is a structure (called frame) defined on a set T and H is a set of (partial) valuations for S on T. It is logical iff (i) if v ∈ H, e is a substitution in S, then v e ∈ H, where v e (t, a) = v(t, ea) and (ii) if v,w ∈ H and v(t,p) = w(t,p) for alltand all variables p,then v = w.
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The following should be observed. We shall not try to mate precise what we mean by definability of elements of H in terms of constituents of F thus the two notions we have introduced should be treated as semiformal.
The Thomason interpretation for Nelson logic covers its quantificational variant. Some doubt concerning the adequacy of Thomason semantics was raised in Hazen [19801, however they do not concern the propositional part of the interpretation and thus are not relevant for our considerations.
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© 1988 Springer Science+Business Media Dordrecht
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Wójcicki, R. (1988). Referential Semantics. In: Theory of Logical Calculi. Synthese Library, vol 199. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-6942-2_6
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DOI: https://doi.org/10.1007/978-94-015-6942-2_6
Publisher Name: Springer, Dordrecht
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