### 24 Semantics of Formulae

Let be the “meaning” function from to (set of Boolean values, ) and let be an interval then

Example 17

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Example 18

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Let denote that the intervals and are identical with the possible exception of the mapping for the variable .

Example 19 Let and be intervals.

• Let and .

Let and .

Let and .

• Let and .

Let and .

Let and .

Then .

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The semantics of is defined in terms of

Example 20

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The semantics of ‘chop’ is as follows

Interval is a fusion of two intervals (satisfies ) and (satisfies ). State is shared by both.

Interval is infinite and satisfies , so is irrelevant.

The semantics of ‘chopstar’ is as follows

Finite interval is the fusion of a finite number of finite sub-intervals each satisfying .

Infinite interval is the fusion of a finite number of sub-intervals each satisfying . Each sub-interval is finite except the last one which is infinite.

Infinite interval is the fusion of an infinite number of finite sub-intervals each satisfying .

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