Based on Carl Jung's descriptions of the thinking functions in his book, "Psychological Types", it seems like they are more about evaluating decision methods rather than being logical. This is especially for Te, which seems to mainly be about ensuring that methods have effective outcomes. Jung categorized Sensing/Intuition into the irrational types and Thinking/Feeling into the rational types, so Thinking/Feeling are about assessing decisions-- "Thinking" is assessing the decision method and "Feeling" is assessing the decision value.
He also described any extraverted function as looking outside of oneself, so Te and Fe assess the decision outcome-- Te specifically focuses on external evidence of effectiveness when assessing a decision method.
Introverted functions are based on the subjective-- understanding that comes from within oneself-- so it sounds like Ti and Fi are about understanding a decision (Ti understands the personal reasoning for choosing certain decision methods, Fi understands the personal value of a decision). Ti is about understanding the method, specifically using personal reasoning and one's personal understanding when assessing a decision method.
Being "logical," therefore, is more of a byproduct of Te/Ti usage, or a consequence of using Te/Ti appropriately-- Te can draw a logical conclusion based on how effective the outcome of a decision method is, Ti can draw a logical conclusion based on how one can personally understand the reasoning behind a decision method. Doesn't mean a logical conclusion is always reached, however. Just as "Feeling" isn't all about emotions, "Thinking" isn't all about logic...it seems like emotion and logic are consequences and/or common influences for feeling and thinking, respectively. And most important, being logical and emotional are personality traits, not cognitive functions, otherwise Jung would have called it "Logic" rather than "Thinking." Anyone can be logical when using any function-- heck, Fi can be logical if one has a rational/logical basis for adopting personal values, and that can be more logical than the Ti user who has a false conclusion about a method just because of poor personal understanding.
So in sum, Thinking seems to be more about assessing the methods of a decision, with Te ensuring effectiveness of the methods and Ti using personal reasoning to understand the methods. Any use of logic is often an influencing factor and/or a consequence, rather than being a characteristic of the function itself. Same goes for emotion in feeling-- its an influencing factor or consequence rather than a characteristic of the feeling function. Overall:
Thinking= prefers assessing decision methods; judges "what makes sense"
Te = ensuring methods for decision outcomes are effective
Ti = understanding personal reasons for choosing decision methods
Feeling= prefers assessing decision value; judges "what is meaningful"
Fe = ensuring decision outcomes are valued by others
Fi = understanding the personal value in a decision
Does anyone agree/disagree with this?