This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. 

This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown. 

http://liarparadox.org/Liar_Paradox_Research_Gate.pdf 

http://philpapers.org/archive/OLCFST.pdf 

https://www.researchgate.net/publication/307442489_Formalizing_the_logical_self-reference_error_of_the_Liar_Paradox