cide with i, but instead overlapped,2 partially or totally, with i. Event types have internal temporal structure that render this distinction important. In the case of primitive event types, that structure is simple. Each primitive event type is derived from a predicate. If  is a predicate, then  denotes the primitive event type derived from . A primitive event type  holds of an interval if the corresponding predicate  holds of every instant in that interval.3 This means that :(i) and :i might have different truth values. For example, if  is true of every instant in [0; 2) and false of every other instant, then :([1; 3)) is true while :[1; 3) is false. Event logic takes coincidental occurrence to be a primitive notion. As will be demonstrated below, overlapping occurrence is a derived notion that can be expressed in terms of coincidental occurrence using compound event-logic expressions.

Two auxiliary notions are needed to define the syntax and semantics of event logic. First, there are thirteen possible relations between two intervals. Following Allen (1983), I denote these relations as =, <, >, m, mi, o, oi, s, si, f, fi, d, and di and refer to them collectively as Allen relations throughout the paper. The names m, o, s, f, and d are mnemonics for meet, overlap, start, *finish*,
and *during* respectively. The inverse relations, such as mi, whose names end in i are the same as the corresponding relations, such as m, whose names do not end in i except that the arguments are reversed. Figure 8 depicts all thirteen Allen relations graphically. Second, I define the span of two intervals i and j, denoted SPAN(i; j), as the smallest super-interval of both i and j.

The syntax of event logic is defined as follows. We are given finite disjoint sets of constant symbols along with a finite set of primitive event-type symbols, each of a specified arity. Constant symbols, such as **red-block** and **hand**, denote objects in the input movie while primitive event-type symbols, such as SUPPORTS, denote parameterized primitive event types. An atomic event-logic expression is a primitive event-type symbol of arity n applied to a sequence of n constants. For example, SUPPORTS(hand; **red-block**). An event-logic expression is either an atomic event-logic expression or one of the compound event-logic expressions :,  _ 	,  ^R 	, or 3R, where and 	 are event-logic expressions and R  f=; <; >; m; mi; o; oi; s; si; f; fi; d; dig.

Informally, the semantics of compound event-logic expressions is defined as follows:
 : denotes the non-occurrence of . An occurrence of : coincides with i if no occurrence of  coincides with i. Note that (:)i could be true, even if an occurrence of  *overlapped* with i, so long as no occurrence of  *coincided* with i.

## _ 	 Denotes The Occurrence Of Either  Or 	.

  ^R 	 denotes the occurrence of both  and 	. The occurrences of  and 	 need not be simultaneous. The subscript R specifies a set of allowed Allen relations between the occurrences of  and 	. If occurrences of  and 	 coincide with i and j respectively, and irj for some r 2 R, then an occurrence of  ^R 	 coincides with the span of i and j. I abbreviate the special case  ^f=g 	 simply as  ^ 	 without any subscript.  ^ 	 describes an aggregate event where both  and 	 occur simultaneously. I also abbreviate the special case  ^fmg 	 as ; 	. ; 	 describes an aggregate event where an occurrence of  is immediately followed by an occurrence of 	.