Download e-book for kindle: A Compositional Semantics for Multiple Focus by Manfred Krifka, Austinlsaarbriicken

Download e-book for kindle: A Compositional Semantics for Multiple Focus by Manfred Krifka, Austinlsaarbriicken

By Manfred Krifka, Austinlsaarbriicken

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Example text

Define d' = U X; we shall show that X =prD ( d') . By definition X:::; d' and X c;; ;, Pre PD,E,), so X c;; ;, prD( d' ). We show the converse inclusion. Let 0, e prD ( d'), then 0,:::; d' =U X and so by prime algebraicity there exists such 02 e X that 0, :::; 02' and so 0, ~D,E,). 3). ° Also, since 0, e prD(d'), 2 :::; d' = U X :::; U prD(d) =d, by prime algebraicity, and so it follows that 0, :::; d and so 0, e prD(d). But we also have X

DEFINITION. 3 (5). 3 (4) are merely mirror images of each other. 7. DEFINITION. 0, < O2 ~ (0, --+ O2 ) 1\ -,(0 2 --+ 0,) then 0, < O2 may be read '0, strictly precedes 0/ It is easy enough to show that < is a strict pre-order - that is to say, a transitive, irreflexive relation and co is an independence relation. 8. PROPOSITION. In any behavioural presentation, two occurrences are either 1- 234- strictly ordered in time; simultaneous concurrent; mutually exclusive Semantics of Parallelism 24 but only one of these relations holds.

As a candidate for P3' we look for the 'smallest' point containing both Pl and 01. Since 02 ~ 01' this point needs to have Pl U { 01} as a subset and contain all its predecessors. Such a set may be obtained using the left-closure operator which we now define. 9. DEFINITION. Let X ~ 0, we define its left-closure, written J,B X to be the set {o E 0 13o' E X: °}, ° °~ 0' }. ° If X = { EO, then we write J, B for J, BX. We shall drop the subscript when there is no danger of confusion. We list some consequences of the definition.

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A Compositional Semantics for Multiple Focus by Manfred Krifka, Austinlsaarbriicken


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