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Mereological theories of events usually assume that the domain of events forms a join semilattice with no bottom element.(Landman 2004's "Indefinites and the Type of Sets" is one of the few exceptions I've found.) There are probably good reasons that most researchers assume that there is no bottom element - i.e., I assume that there are negative consequences to assuming a bottom element, and that these have been discussed somewhere in the literature.

What are some of these negative consequences? (Or where could I find a discussion of some of them?)

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    I cannot understand the question. The content strikes me as specific to a particular theory of semantics, which means it may be difficulty to find someone with the knowledge to answer it. – Tim Osborne Nov 27 '13 at 18:41
  • I know little of Mereological theories of events, but the absence of a bottom element may be either because there are several minimal elements or because there are infinite decreasing chains (or both). Which is it for the theories you are concerned with? I do not see why the former should be less a problem than a single bottom elements, which could possibly be added. On the other hand, allowing infinitely decreasing chains may be essential for some semantic theories, though this may raise constructiveness issues. – babou Dec 1 '13 at 15:06
  • @babou, they assume that the domain of events has the structure of a boolean algebra, with the bottom element removed. So there are several minimal elements. I know that removing the bottom element allows for a simpler definition of the overlap relation - eg., where two elements overlap if they share a subpart. If the bottom element is present with this definition, then everything overlaps. But don't think there's a huge problem in redefining overlap so it requires that they share a non-null part. But I thought there might be other, less fixable, consequences. – user177 Dec 4 '13 at 2:49
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For a mereological approach with a bottom element see Link (1983). For reasons why the bottom element is not desirable see Link (1998:284ff). He discusses this at length when talking about processes. Specifically: "[...]processes are mereologically structured entities that form my basic particulars. I assume that their mereology is classical, but not explicitly atomic. In particular, there is no such thing as "the null process," i.e., the process lattice doesn't have a bottom element.". This is not very specific, but I would suggest you read that subsection to get a feeling for the philosophical arguments against a bottom element.

There are other reasons for not wanting a bottom, which I prefer. A simple one is, when dealing with spatial entities (e.g. point in space linked to events, as most event structures assume them nowadays), you would not want to assume there to be something that is a part of everything (which bottom is), committing us to an overlap across the domain -- which is implausible. This is my own reason and also the one given in (Geach 1949, Simons 1987, Lewis 1991 and Varzi 2007).

So the reason is more why you'd want a bottom, rather than why you would not want one. Technically we don't lose much without it, as we still get structure isomorphic to a complete Boolean algebra with the zero element removed (as shown in Tarski 1935).

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