The work closest to the present is [Pin98b], as one of the referees forcefully pointed out. There are substantial differences, both in approach and in the formalisms motivated by the different approaches.
Pinto uses the Reiter notion of situations as trees built from the initial situation S0 by iterations of forming do(a,s) where a is an action and s a previously formed situation term.
Pinto (as does Reiter) builds time, represented by a real number, into his situation calculus formalism. It seems to me that making time fit the tree structure of situation terms leads to complications. Pinto has five different occur predicates, whereas we have only one. His occurrence axioms all have time parameters. Our occurrence axioms involve only situations and fluents and are therefore simpler. The examples of the present article do not involve time explicitly. When time must be explicit, we propose to treat the passage of time as an independent situation calculus process running concurrently with the processes we are treating.
Pinto includes the following interesting examples. We show how our method treats a few of them.
1. ``The sun will rise tomorrow at 6:03 am.'' Here we have two concurrent processes: the passage of time and the path of the sun through the sky. The sentence describes an interaction.
We can represent the sentence by
where we are not taking into account the explicit indexical of tomorrow, and the implicit indexical that sunrise being a 6:03am must refer to a specific latitude and longitude.
2. ``If you eat the forbidden fruit you will be expelled.'' Pinto treats this as one event causing another but remarks that it might be better formalized as a state, i.e. that of having eaten the fruit, giving rise to an event. That's how the present paper would treat it, i.e.
together with the general moving finger axioms
3. ``The train to Ottawa leaves every day at 7 pm.'' where it is understood that this scheduled event may not occur under exceptional circumstances.
4. ``If my neighbor's burglar alarm goes off while I am at home, I will call the police.'' Pinto treats this example and the previous one by slightly different formalisms, one involving a predicate and the other a predicate .
5. The Miller-Shanahan [RM94] example of the briefcase.
6. ``My house has a burglar alarm. If the alarm is connected, I have exactly 60 seconds to deactivate it after opening the main door. If I am unable to disconnect the alarm, it will go off.''
7. ``Upon an insertion into EMP or an update to EMP, the new SAL is checked, and if it exceeds $100,000, then the JobTitle of this employee is added to HPAID, assuming it was not there already.''
[Pin98a] introduces occurs(a,s), where a is a ``natural action''. Natural actions partly correspond to internal events. The article is dedicated to concurrent events, to which I hope devote a separate article.