Full Idea
KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts.
Clarification
The Liar sentence says 'this sentence is false'
Gist of Idea
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts
Source
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.11
A Reaction
[summary, which I hope is correct! Stanford is not wholly clear]