Abstract
In this concluding chapter, we will glance at some possible developments of our theory of generalized truth values. In particular, we will raise the issues of adding quantifiers and modal operators to the propositional languages considered in the previous chapters. Moreover, we will briefly touch on the idea of adverbially qualified truth values. Finally, we will look at further philosophical interpretations of Dunn and Belnap’s four-valued logic and consider the possibilities of an extension of these interpretations beyond the four-valued case.
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- 1.
The familiar ◊-version of the necessitation rules is \(\vdash \neg A / \vdash \neg \,\lozenge A,\) and the familiar ◊-version of the \(K\) axiom is the formula \((\neg \,\lozenge A \wedge \,\lozenge B) \rightarrow \,\lozenge (\neg A \wedge B),\) cf. [51, Chap. 4]. Since we have two versions of negation, conjunction, and implication in \({{\fancyscript{L}}}^{*}_{tf},\) there are \(several\) options for formulating “◊-versions” of the necessitation rule and the \(K\)-axiom.
- 2.
Lewis uses the term “discursive” from the first English translation of Jaśkowsi’s paper, but “discussive” seems to be the more appropriate translation of the Polish word “dyskusyjny”, see the editorial note in [135, p. 55].
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© 2011 Springer Science+Business Media B.V.
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Shramko, Y., Wansing, H. (2011). Further Developments. In: Truth and Falsehood. Trends in Logic, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0907-2_10
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DOI: https://doi.org/10.1007/978-94-007-0907-2_10
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