A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.