|Norvig I 545
Open Universe/probabilities/environment/AI research/Norvig/Russell: (…) a major part of human cognition seems to require learning what objects exist and being able to connect observations - which almost never come with unique IDs attached - to hypothesized objects in the world. For these reasons, we need to be able to write so-called open-universe probability models or OUPMs based on the standard semantics of first-order logic (…).
A language for OUPMs provides a way of writing such models easily while guaranteeing a unique, consistent probability distribution over the infinite space of possible worlds. (>Bayesian networks/Norvig).
The basic idea is to understand how ordinary Bayesian networks and RPMs ((s) Relational probability models; >Bayesian networks/Norvig) manage to define a unique probability model and to transfer that insight to the first-order setting. In essence, a Bayes net generates each possible world, event by event, in the topological order defined by the network structure, where each event is an assignment of a value to a variable. An RPM extends this to entire sets of events, defined by the possible instantiations of the logical variables in a given predicate or function. OUPMs go further by allowing generative steps that add objects to the possible world under construction, where the number and type of objects may depend on the objects that are already in that world. That is, the event being generated is not the assignment of a value to a variable, but the very existence of objects. One way to do this in OUPMs is to add statements that define conditional distributions over the numbers of objects of various kinds._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010