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Gupta Truth

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             Revision theories and contextual theories both offer a solution which can be applied to natural languages. Revision theories use a scheme whereby a hypothetical extension for the truth-predicate is proposed and successively improved by stages. Contextual theories give their solution by treating the truth-predicate as indexically defined.
             5.2 Fixed-point Theories.
             Some three-valued systems contain an additional truth-value n, which can be interpreted as neither-true-nor-false. Gupta introduces a semantics for this new truth-predicate which is based on the classical system and which respects the classical values assignments in the standard cases. The set of truth-values can be given an information ordering with n being the least element and t and f being incomparable. This ordering can be extended first to the predicates, then to the sentences, and finally to the models of the system. The ordering gives rise to the property of montonicity in the system. This means that two models can be at least as informative as one another iff they have the same domain and interpretation, and the model with the least number of classical truth-value assignments agrees on all of these assignments with the other (which can have more classical assignments) Creating a truth-predicate T in the three value language L+ requires setting the extension of T to all and only the true sentences of L. L is a language just like L+ except it does not contain the predicate T. Further, the domain of L+ contains all the sentences of L. The anti-extension of T is defined as the set of all sentences which come out false in L. Two sets can be named that correspond to the extension and anti-extension of T in L; we call them U and V respectively. These sets are populated according to the value assignment given by some unique Val. function h. A Strong Kleene jump can be defined as a function on this Val function which produces new sets corresponding to those sentences which come out true in L+.


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