Theory of Logical Calculi pp 341-401 | Cite as

# Referential Semantics

Chapter

## 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 all*t*and all variables *p*,then *v* = *w*.

## Keywords

Modal Logic Boolean Algebra Intuitionistic Logic Completeness Theorem Modal Algebra
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## References

- 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.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