Stanford Encyclopedia (2014)
Truth is the aim of inquiry. Nevertheless, some falsehoods seem to realize this aim better than others. Some truths better realize the aim than other truths. And perhaps even some falsehoods realize the aim better than some truths do. The dichotomy of the class of propositions into truths and falsehoods should thus be supplemented with a more fine-grained ordering — one which classifies propositions according to their closeness to the truth, their degree of truthlikeness or verisimilitude. The logical problem of truthlikeness is to give an adequate account of the concept and to explore its logical properties. Of course, the logical problem intersects with problems in both epistemology and value theory.
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I agree with you to use similarity or distance to define Truthlikeness function.
Yet I use some different method.
For exampe, a hypothesis hj="His age is about 20 years old".We can use T(hj|E)=exp[-(E-20)2/8] as truth function or  Truthlikeness function..
If we wish that  Truthlikeness can tell precision and give tautology lower Truthlikeness,  we may use 
T(hj|E)/T(hj)  or I=log[T(hj|E)/T(hj)] as Truthlikeness, where T(hj)=sum i P(ei)T(hj|ei) is the average of T(hj|E), and may be call logical probability of hj.

For more details, see my paper: 
Semantic Information Measure with Two Types of Probability for Falsification and Confirmation