When determining a price for a journey, the price is a function of the availability on each individual flight. The availability loosely corresponds to the number of seats that have been sold and to the number that are still unsold. But really it is a tool that can be actively used to manage supply. The airline will open cheap seats if demand is weak and close cheap seats if they forecast demand to be strong.
But airlines sell journeys, they do not sell flights. [Except for a few low cost carriers which I ignore here.] So if you have a short flight that is getting full, you might want to say, "we don't sell any more cheap seats on that flight". However if that short flight can be used to connect to a longhaul, highly profitable flight, you still want to keep the short flight open to people going on the longhaul flight.
In this case the segments are "married": when you say to the airline "how many seats are for sale on flight 123?" the airline says "that depends what other flights you want to buy".
For instance, let us suppose you are looking at Qatar Airways flight 1021 from Dubai (DXB) to Doha (DOH) tomorrow. The availability, in isolation, of that flight is
F1 PL AL Y9 B9 H4 K4 M4 L4 V4 S4 N4 Q4 T2 OC WC. The first class fare buckets (F, P, A) are looking very busy, with just one seat for sale in the most expensive bucket (F). The others are "list only", i.e., you can join the waiting list if you want but a seat is not presently available.
However if you are interested in flying onwards to London, the availability of QR 1021 now becomes
F2 P2 A2 Y9 B9 H9 K9 M9 L9 V9 S9 N4 Q4 T4 O3 WC --- suddenly Qatar have found another first class seat, and what's more they'll offer it to you at a lower fare. But only if you are travelling onwards to London.
That's because the purpose of shorthaul flights is for feeding longhaul. So it makes no sense to fill up your shorthaul flights with local traffic. You need to keep seats available for those connecting to your profitable longhaul services.
You cannot really identify married segment logic except by individual inspection of the availability of the flight on its own and in combination with other flights. The exact inner logic of each airline's married segment logic will be a trade secret based on their own data analysis. The logic is not expressed in the fare rules.
For the most part the ITA Matrix understands married segment logic as well as any other flight search engine (or perhaps better). However you may find that some other search engines "slice" their search query in a different way, giving different results. A travel agent who understands this well can do a manual sell from the airline directly or alternatively play around with the search until it performs as expected.