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Programming logic is a fundamental construct that's applied to computer science in a variety of comprehensive ways.
Programming logic involves logical operations on hard data that works according to logical principles and quantifiable results.
The term programming logic has its roots in the advancement of computer science. Programming logic started only with 'hard and fast logic’ compiled into sophisticated algorithms and expressed in programming languages like Prolog.
Basic computers developed ways to deal with numbers and logical states, applying specific operators that lead to precise results.
The important distinction here is that programming logic, and logic in general, is fundamentally set against other kinds of programming that are not built on hard logic or quantifiable states and results.
For example, modal logic by its nature is set against the theoretical quantum operations that don't provide a specific set state that computers can apply logic to.
Programming logic in general rests on a foundation of computational logic that is shared by both humans and machines, which is what we explore as we continue to interact with new technologies. With that in mind, one could develop more specific definitions of a programming logic having to do with the basis of a piece of code.