Well, I think that observations can be both our reasoning and sensory data.

Suppose you have a model* of your own accuracy at addition of integers, which is that you are 95% likely to get the correct answer, 2% to be one high, 2% to be one low, and with the remaining 1% divided somehow amongst other possibilities. Then, when you actually observe that when adding 2 + 2 you get 4, this is Bayesian evidence that gives a likelihood ratio of 42.5 : 1 in favor of the theory that 2 + 2 = 4 compared to the theory that 2 + 2 = 3.

Now suppose you have a collection of pebbles, and your model of the pebbles claims that if you count out 2 distinct collections of pebbles, and then combine them and count the total, that the sum of the counts of the distinct collections is 90% likely to be the count of the combined collection, and is 4% likely to be one high, 4% to be one low, and 2% to be something else. And then you actually count out a collection of 2 pebbles, and another collection of 2 pebbles, and combine them, and when you count the combined collection you count 4 pebbles. This is Bayesian evidence with a likelihood ratio of 22.5 : 1 in favor of 2 + 2 = 4 as opposed to 2 + 2 = 3.

In both cases, belief in a logical proposition results from our belief that an observable system has some probability of reflecting logical truth. If, as in the example numbers that I made up just now, we believe that our reasoning process is more likely than observations of our environment, then the results of our reasoning is stronger evidence, but it is still the same class of evidence.

* I have neglected the harder problem of simultaneously updating propositions about additions and propositions about a given system's probability of representing addition. That is, I have not explained where the models I asked you suppose you have really should come from.