Well, as I said my understanding of logic is fairly basic. I'm sure however that there is no agreed upon consensus on exactly what logic is.
To me logic is the calculative element of information or meaning, the other parts being values and syntax. You can't really have information without either, and I'd even question if separating them is possible. I mean, I can say "blueberry" and it carries a value, but there has to be a calculation somewhere that ensures the word can carry that value - and there has to be a syntactic element for us to know how to set up the word. But all these elements are interacting and it doesn't seem intuitive to me that they can do anything without each-other. Or in simpler terms: At any point where we try to reduce the concepts of information or meaning into parts, we have to use information and meaning to describe those parts.
To use an analogy: If I paint a picture, the final picture is the information or meaning. Logic is how the paint behaves on the canvass, syntax is the patterns necessary for the painting to portray something and values is the things we want to paint. But the concept of a painting becomes meaningless without those elements, so we're just in a spiral of endless definitions if we try to figure out exactly what it is.
But at this point I don't even know if I'm making sense or using terms in some manner which contradicts great thinkers.