Temporal Reasoning with Probabilities

TL;DR

This paper introduces two continuous-time probabilistic models for representing temporal knowledge, emphasizing the importance of explicitly modeling different types of temporal relations and proposing methods to embed these in causal probabilistic networks.

Contribution

It proposes novel continuous-time representations for temporal reasoning within Causal Probabilistic Networks, including methods to explicitly model various temporal relations.

Findings

Two continuous-time CPN representations are proposed.

Explicit modeling of different temporal relations improves reasoning.

Method for embedding diverse temporal relations using auxiliary nodes.

Abstract

In this paper we explore representations of temporal knowledge based upon the formalism of Causal Probabilistic Networks (CPNs). Two different ?continuous-time? representations are proposed. In the first, the CPN includes variables representing ?event-occurrence times?, possibly on different time scales, and variables representing the ?state? of the system at these times. In the second, the CPN describes the influences between random variables with values in () representing dates, i.e. time-points associated with the occurrence of relevant events. However, structuring a system of inter-related dates as a network where all links commit to a single specific notion of cause and effect is in general far from trivial and leads to severe difficulties. We claim that we should recognize explicitly different kinds of relation between dates, such as ?cause?, ?inhibition?, ?competition?, etc., and propose a method whereby these relations are coherently embedded in a CPN using additional auxiliary nodes corresponding to "instrumental" variables. Also discussed, though not covered in detail, is the topic concerning how the quantitative specifications to be inserted in a temporal CPN can be learned from specific data.