Conditional Values in Signed Meadow Based Axiomatic Probability Calculus

An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values and configurations. Assuming the presence of a probability function, equational axioms are provided for expectation value, variance, covariance, and correlation squared, each for conditional values, and for expected utility of configurations. Finite support summation is introduced as a binding operator on meadows which simplifies formulating requirements on probability mass functions with finite support. Conditional values are related to probability mass functions and to random variables. The definitions are reconsidered in a higher dimensional setting.