A Semantics for Probabilistic Quantifier-Free First-Order Languages, with Particular Application to Story Understanding

We present a semantics for interpreting probabilistic statements expressed in a first-order quantifier-free language. We show how this semantics places constraints on the probabilities which can be associated with such statements. We then consider its use in the area of story understanding. We show that for at least simple models of stories (equivalent to the script/plan models) there arc ways to specify reasonably good probabilities. Lastly, we show that while the semantics dictates seemingly implausibly low prior probabilities for equality statements, once they are conditioned by an assumption of spatio-temporal locality of observation the probabilities become "reasonable."