Semiring Semantics

Explore a comprehensive lecture on semiring semantics delivered by Erich Graedel from RWTH Aachen at the Simons Institute. Delve into the concept of evaluating logical statements using values from commutative semirings, extending beyond traditional true or false assessments. Discover how this approach provides additional information such as costs, confidence scores, and access levels. Examine the use of polynomial and formal power series semirings to track atomic fact usage in establishing sentence truth. Trace the evolution of semiring semantics from its origins in provenance analysis for positive database query languages to its current applications in first-order and fixed-point logic. Investigate the extent to which standard model-theoretic and algorithmic results from classical logic can be extended to semiring semantics, and analyze how these extensions depend on the chosen underlying semiring. Gain insights into the intersection of logic and algebra in query evaluation through this hour-long exploration of advanced semantic concepts.