A Logic-Based Approach to Activity Recognition

2. The Event Calculus

Our Long-Term Activity Recognition (LTAR) system consists of a logic programming (Prolog) implementation of an Event Calculus dialect. The Event Calculus, introduced by Kowalski and Sergot (1986), is a many-sorted, first-order predicate calculus for representing and reasoning about events and their effects. For the dialect used here, hereafter LTAR-EC (event calculus for long-term activity recognition), the time model is linear and it may include real numbers or integers. Where F is a fluent – a property that is allowed to have different values at different points in time - the term F = V denotes that fluent F has value V. Boolean fluents are a special case in which the possible values are true and false. Informally, F = V holds at a particular time-point if F = V has been initiated by an event at some earlier time-point, and not terminated by another event in the meantime.

An event description in LTAR-EC includes axioms that define, among other things, the event occurrences (with the use of the happensAt and happensFor predicates), the effects of events (with the use of the initiatedAt and terminatedAt predicates), and the values of the fluents (with the use of the initially, holdsAt and holdsFor predicates). Table 1 summarises the main predicates of LTAR-EC. Variables, starting with an upper-case letter, are assumed to be universally quantified unless otherwise indicated. Predicates, function symbols and constants start with a lower-case letter.