Semirings of Evidence

TL;DR

This paper introduces a new semantic framework for justification logic using semirings to model evidence, enabling algebraic computation and broad applications like trust and probability modeling.

Contribution

It presents a novel semiring-based semantics for evidence in justification logic, allowing algebraic manipulation and interpretation of evidence terms.

Findings

Provides a semantics where evidence is modeled by semirings

Enables computation with evidence using algebraic structures

Potential for applications in trust, probability, and modal fixed point logics

Abstract

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics.