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2.3 State and eventtype reification


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The method of state and eventtype reification was introduced to cater for distinctions of this kind. It is an approach that has been especially popular in Artificial Intelligence, where it is particularly associated with the name of James Allen, whose influential paper (Allen 1984) is often cited in this connection. In this approach, state and event types are denoted by terms in a firstorder theory; their temporal incidence is expressed using relational predicates “Holds” and “Occurs”, as for example,
Holds(Asleep(Mary), (1pm, 6pm))where terms of the form (t, t′) denote time intervals in the obvious way.
Occurs(Walkto(John, Station), (1pm, 1.15pm))
The homogeneity of states and inhomogeneity of events is secured by axioms such as
∀s, i, i′(Holds(s, i) & In(i′, i) → Holds(s, i′))where “In” expresses the proper subinterval relation.
∀e, i, i′(Occurs(e, i) & In(i′, i) → ¬Occurs(e, i′))
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<h3>2.3 State and eventtype reification</h3> The method of temporal arguments encounters difficulties if it is desired to model <em>aspectual</em> distinctions between, for example, states, events and processes. Propositions reporting states (such as “Mary is asleep”) have <em>homogeneous</em> temporal incidence, in that they must hold over any subintervals of an interval over which they hold (e.g., if Mary is asleep from 1 o'clock to 6 o'clock then she is asleep from 1 o'clock to 2 o'clock, from 2 o'clock to 3 o'clock, and so on). By contrast, propositions reporting events (such as “John walks to the station”) have inhomogeneous temporal incidence; more precisely, such a proposition is not true of <em>any</em> proper subinterval of an interval of which it is true (e.g., if John walks to the station over the interval from 1 o'clock to a quarter past one, then it is not the case that he walks to the station over the interval from 1 o'clock to five past one — rather, over that interval he walks part of the way to the station). <p> The method of state and eventtype reification was introduced to cater for distinctions of this kind. It is an approach that has been especially popular in Artificial Intelligence, where it is particularly associated with the name of James Allen, whose influential paper (Allen 1984) is often cited in this connection. In this approach, state and event types are denoted by terms in a firstorder theory; their temporal incidence is expressed using relational predicates “Holds” and “Occurs”, as for example,</p> <blockquote>Holds(Asleep(Mary), (1pm, 6pm)) <br> Occurs(Walkto(John, Station), (1pm, 1.15pm))</blockquote> where terms of the form (<em>t</em>, <em>t</em>′) denote time intervals in the obvious way. <p> The homogeneity of states and inhomogeneity of events is secured by axioms such as</p> <blockquote>∀<em>s</em>, <em>i</em>, <em>i</em>′(Holds(<em>s</em>, <em>i</em>) & In(<em>i</em>′, <em>i</em>) → Holds(<em>s</em>, <em>i</em>′)) <br> ∀<em>e</em>, <em>i</em>, <em>i</em>′(Occurs(<em>e</em>, <em>i</em>) & In(<em>i</em>′, <em>i</em>) → ¬Occurs(<em>e</em>, <em>i</em>′))</blockquote> where “In” expresses the proper subinterval relation. 
