Semirings of Evidence

Baur, Michael; Studer, Thomas (April 2020). Semirings of Evidence. In: Dastani, Mehdi; Dong, Huimin; van der Torre, Leon (eds.) Logic and Argumentation. International Conference, CLAR 2020, Proceedings. Lecture Notes in Computer Science: Vol. 12061 (pp. 42-57). Springer 10.1007/978-3-030-44638-3_3

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In traditional justification logic, evidence terms have the syn-tactic form of polynomials, but they are not equipped with the corre-sponding algebraic structure. We present a novel semantic approach tojustification logic that models evidence by a semiring. Hence justificationterms can be interpreted as polynomial functions on that semiring. Thisprovides an adequate semantics for evidence terms and clarifies the roleof variables in justification logic. Moreover, the algebraic structure makesit possible to compute with evidence. Depending on the chosen semiringthis can be used to model trust, probabilities, cost, etc. Last but notleast the semiring approach seems promising for obtaining a realizationprocedure for modal fixed point logics

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