4
Since the private key is needed to validate ownership, how does it work when you cannot access the private key?
Say X owned bitcoins and willed it to Y, but Y does not have X's private key. Say X's estate does not want to to give access to the private key or the location of the private key is untraceable.
4
Y can't spend the Bitcoins. You need the private key for an address to spend the Bitcoins from that address. There's no way around it.
2
It would be possible to use a multisignature scheme in order to will the bitcoins.
A 2 out of 3 multisignature address would be shared among three keys controlled by the bequeather X, the heir Y, and a trusted third party Z, for example the notary of X.
Any two parties of the three could move the money:
As Nick has pointed out, this would have to be done before the demise of the Bequeather, otherwise access would fall to whoever ended up in control of the private key, or the bitcoins would be lost if no-one regained it.
1I've slightly improved your answer to make it a bit easier to understand. Please feel free to reverse any changes I've made or further improve it to your liking. – Murch – 2014-12-12T16:45:50.390
Please clarify what "PK" do you use. Is it "Private Key" or "Public Key"? – amaclin – 2014-12-11T08:07:43.793
PK = Private key – Suminda Sirinath S. Dharmasena – 2014-12-11T08:25:31.553
This may be interesting, even if it is pretty much purely theoretical: https://en.bitcoin.it/wiki/Contracts#Example_4:_Using_external_state
– Tyler – 2014-12-12T20:47:32.273related: What happens to my bitcoins when I die?
– Murch – 2015-03-29T15:35:10.730