In this paper, we propose a new version of complete logic—Ŀogic of İnexact K̇nowledge ( \(\textsf{LIK}\) )—that has the following eight features out of which the seven can reflect Williamson (1994)’s arguments but out of which the only one is essentially different from the features based on Williamson’s knowledge first epistemology: 1. This model based on additively-semiordered qualitative conditional probability that is a qualitatively-probabilistic counterpart of a JND which is a psychophysical counterpart of a margin for error can reflect the essence of inexact knowledge. 2. We can formalize a margin for error principle in \(\textsf{LIK}\) . 3. The width of a margin for error (JND) depends on the cognitive capacities. 4. In \(\textsf{LIK}\) , the direct indiscriminability relation is a non-transitive relation. 5. The reason why we introduce qualitative not absolute but conditional probability is to make it possible to express the direct indiscriminability between the two events on the condition that either of the two occurs. 6. \(\textsf{LIK}\) has so rich expressive power as to fully formalize such inferences as (6)–(8). 7. The KK principle is not valid in \(\textsf{LIK}\) . 8. Essential Difference: In Williamson’s \(\textsf{LC}\) inexact knowledge is primitive based on his knowledge first epistemology, whereas in \(\textsf{LIK}\) inexact knowledge is defined in terms of the direct indiscriminability relation based on our direct indiscriminability relation first epistemology.