Can you explain an intuition behind Coherent Spaces?
The intuition behind coherence spaces is that the elements of a coherence space represent observations of some underlying data, and the coherence relation tells you whether two observations could have come from the same piece of data.

Concretely, suppose we have a set of animals

Animals = {cat, duck, fish}


Now, we can have a set of observations:

Observations = {warm-blooded, swims, water-breathing, furry}


Let us say that two observations are compatible if they could both be made of the same animal. Every observation is compatible with itself, and in addition:


warm-blooded $\stackrel{{\large\frown}}{{\small\smile}}$ furry
warm-blooded $\stackrel{{\large\frown}}{{\small\smile}}$ swims
warm-blooded $\stackrel{{\large\frown}}{{\small\smile}}$ furry
swims $\stackrel{{\large\frown}}{{\small\smile}}$ water-breathing


We know that being warm-blooded is compatible with swimming, because ducks are both warm-blooded and swim. But being warm-blooded and water-breathing are not compatible, since we have no animals which are both warm-blooded and water-breathing.

At this point, we have defined a coherence space (Observations, $\stackrel{{\large\frown}}{{\small\smile}}$), where Observations is the web, and $\stackrel{{\large\frown}}{{\small\smile}}$ is the coherence relation.