There are many ways that property can be owned other than by natural persons (not necessarily businesses).
Property can be owned by entities and other legal personalities (such as corporations, corporations sole, limited liability companies, limited partner associations, nominees, non-profit corporations, cooperatives, partnerships, limited partnerships, limited liability partnerships, limited liability limited partnerships, trusts, business trusts, estates, conservatorships, governmental entities, unincorporated associations, tontines, funds, etc.), as well as by natural persons. Ownership of property by something other than natural persons dates, at least, to the Song Dynasty in China and to at least the 13th century in Europe.
A good modern example is MERS which is the nominee holder of mortgages that are then traded commercially (often electronically, often in transactions not involving humans between entities). A similar example, is street name ownership of a publicly held security within which electronic trades are facilitated.
Even when trusts are not created intentionally, they can be implied in law.
In New Zealand, even a river can have corporate personality (an idea proposed in legal scholarship decades earlier) and thus has legal standing to sue and own property, through a representative appointed by a legal process.
This river can bring lawsuits and own property.
While these entities must be formed by individuals at the outset, some kinds of entities and trusts, such as non-profits and charitable trusts, do not have human "owners" in any meaningful sense. You can also have trusts that are for the benefit of animals or the graves of deceased people.
The issue of "dead hand control" is a long standing one in the law, which was first addressed in the common law tradition in the Duke of Norfolk's Case of 1682 which gave rise to what is known now as the Rule Against Perpetuities (which now has many exceptions).
There is also no prohibition on entities or legal instruments making decisions based upon formulas or programs, indeed, certain kinds of mutual funds (e.g index funds and exchange traded funds), which are generally organized as business trusts, are required to carry out their operational duties in a formulaic manner.
Legal instruments such as deeds creating life estates and residuary estates, joint tenancy deeds, and beneficiary deeds have transferred real property by operation for law for hundreds of years without human intervention at the time of transfer, operating as simple "programs".
Likewise, business transactions are routinely effected electronically without human intervention. Lots of e-commerce is conducted in that manner.
For example, you do that when you use an ATM or go to a self-check out kiosk for a movie or at an airport or in a grocery store. Sometimes these programs are called "electronic agents" but they need not be agents of a natural person, they could also be (and indeed, usually are) agents of a legal personality that is not a natural person.
Even before electronics were invented, vending machines mechanically effected business transactions, transferring title to the personal property contained within them, without human involvement.
An early non-human device that conducted business transactions without electronics. (Similar devices have existed as far back as antiquity in classical Greece, dispensing Holy Water.)
An entity could be formed that transacts principally via blockchain and that entity would not even have to have owners. It would have to have natural persons affiliated with it in some way, but its main businesses could be conducted by a computer system that these affiliated natural persons put into place for an entity that they form.
Legal instruments like paper currency, checks, negotiable promissory notes, bearer bonds, negotiable warehouse receipts, and derivatives all have some of the features associated with blockchains (i.e. incorporating a third-party non-natural person's involvement in a transaction without active management by natural persons).
In general, a blockchain is not a legal innovation and introduces nothing that is legally new or revolutionary. It is old wine poured into new skins.
