Yes, local is plural, because there is often more than one way to think of something. Logic means to think about something reasonably, and in a scientific way. Thinking about something logically does not necessarily mean that there is only one right answer. Rather, plural logic thinks about things in a scientific way, but imagines multiple solutions.
This is a very interesting question. I think that the word "logic" must be plural due to the fact that there is not another plural form of the word that exists. I have never talked about it in a plural sense, but saying "logics" does not make a lot of sense, so therefore logic itself must be plural.
Yes, I think that people can arrive at logic in more than one different way, and can have logic in more than one different area. I think by searching and becoming more knowledgeable with the world that people can then in turn find logic throughout the world, and multiple times in doing so.
Yes, logic is one of many words whose singular and plural forms are the same. Others include Templar and moose. The logical process (both singular terms) hints at several things combined into one. Fact A with Fact B checked against Fact C produce Conclusion 1. As such, the word indicates many functions occurring to reach the end.
Logic can be used to come to many different conclusions. For example, I say Hi to somebody passing the street and they ignore me. I can conclude several different possibilities based on the available evidence; the person didn't hear me, the person intentionally ignored me, for example. There was probably only one reason, but logically you can conclude many possibilities.
People, come on, some of the logic being used here to prove the plurality is horrible. Yes, there is no plural to the word logic, but neither is there one to the word fish or aircraft (apparently). By your logic, this means that every fish is lots of fish and every plane is lots of planes. You cannot use the oddities of English language to debate a philosophical point.