Referential Semantics

  • Ryszard Wójcicki
Part of the Synthese Library book series (SYLI, volume 199)


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 vH, e is a substitution in S, then v e H, where v e (t, a) = v(t, ea) and (ii) if v,wH and v(t,p) = w(t,p) for alltand all variables p,then v = w.


Modal Logic Boolean Algebra Intuitionistic Logic Completeness Theorem Modal Algebra 
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  1. 1.
    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.Google Scholar
  2. 2.
    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.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1988

Authors and Affiliations

  • Ryszard Wójcicki
    • 1
  1. 1.Section of Logic, Institute of Philosophy and SociologyPolish Academy of SciencesPoland

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