A Formal Theory of Justifications

We develop an abstract theory of justifications suitable for describing the semantics of a range of logics in knowledge representation, computational and mathematical logic. A theory or program in one of these logics induces a semantical structure called a justification frame. Such a justification frame defines a class of justifications each of which embodies a potential reason why its facts are true. By defining various evaluation functions for these justifications, a range of different semantics are obtained. By allowing nesting of justification frames, various language constructs can be integrated in a seamless way. The theory provides elegant and compact formalisations of existing and new semantics in logics of various areas, showing unexpected commonalities and interrelations, and creating opportunities for new expressive knowledge representation formalisms.