Announced in "Semantic Considerations on Modal Logic" (1963), and presented in detail in a subsequent series of technical papers, Kripke's work covers modal and intuitionistic sentential and predicate logic, and includes besides completeness theorems results on decidability and undecidability.
Semantic Paradoxes
Also well known is Kripke's work on semantic paradoxes in "Outline of a Theory of Truth" (1975). A truth-predicate in a language L permitting quotation or equivalent means of self-reference would be a predicate T such that the following biconditional holds with any sentence of L in the blanks:
"T('__________')" is true if and only if "__________" is true.
The liar paradox shows there cannot be a truth-predicate in L if L has no truth-value gaps. Given a partial interpretation I of a predicate U (under which U is declared true of some items, declared false of others, or not declared either of the rest), any treatment of truth-value gaps, such as Stephen Cole Kleene's three-valued or Bas van Fraassen's supervaluational approach, will dictate which sentences containing U are to be declared true, declared false, or not declared either. If U is being thought of as "is true," this amounts to dictating a new partial interpretation I* of U.
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