Final answer:
There is no specific formal system known as 'first-person logic', but traditional logic abstracts personal perspectives to universal principles.
Step-by-step explanation:
The question touches upon the concept of first-person logic, which could be considered a part of the study of logic, specifically how it relates to personal perspective in narratives and argumentation.
However, most formal systems of logic, like the one developed by Aristotle and the symbolic logic following Gottlob Frege, typically abstract from the first, second, and third person to focus on universal principles of reasoning applicable to any subject. These systems aim to formalize the process of reasoning and support claims with well-founded arguments.
Systems of logic are deeply connected with the structure of language and reasoning, as exemplified in Frege's work which translates natural language into a symbolic notation to reduce ambiguity. Within philosophical tradition, logic is the normative science of reasoning, governing how we should form arguments and reach conclusions.
While there is no formal system specifically called 'first-person logic', the study of how individual perspectives can be formally represented could be approached from multiple angles within philosophical logic, including modal logic or deontic logic that deals with necessity, possibility, and obligation in relation to agents' perspectives.