Calculating semantic uncertainty

Starting with a psychological definition of semantics, and a representation of semantic information by feature-value pairs, the basic operations decision and conjunction are studied. It is proved that a number of natural requirements concerning consistency with valuation and stability imply that homomorphic images of these operations yield the algebraic structure semiring. As semirings can serve as weights for finite state transducers, this provides a wealth of algorithms applicable on the semantic level. Based on an algebraic difference between feature confidence and value probability, two-component semirings are constructed and linked to psychology via their limiting behavior of conjunction for low resp. high confidence. Finally, the connections between calculations of semantic uncertainty, semantic dialogue modeling, and meaning-oriented language modeling are discussed.