Abstract

The paper develops an axiomatic theory of truth and falsehood operators, including the non-classical case. Their domain is a set of sentences, which then is extended to the set of symbol expressions of the language. In general, sentences do not necessarily have to be two-valued. In case of statements about the truth or falsity of sentences, classical logic is applied. We restrict ourselves to the set of sentences for which the truth and falsehood operators are well-defined. This proposed theory differs from Kripke’s theory of truth. Iterations of truth and falsehood operators are allowed. Thus, the pro-posed theory differs from Tarski’s semantic theory of truth. Note that the use of truth and falsehood operators instead of the corresponding predicates allows avoiding the liar paradox. Non-truthfulness in general does not necessarily mean falsehood. Therefore, truth and falsehood operators will be regarded as logically independent. On the basis of the above considerations, the truth and falsehood operator theory is constructed and formulated and it is further ex-tended to the universe of symbolic expressions.