Is it logical to use “Proof-of-Authority” for a “public” blockchain? According parity.io website: 


  Proof-of-Authority is a replacement for Proof-of-Work, which can be
  used for private chain setups.


And also:


  The chain has to be signed off by the majority of authorities, in
  which case it becomes a part of the permanent record. This makes it
  easier to maintain a private chain and keep the block issuers
  accountable.


And also:


  PoA networks are well-suited to regulated industries where entities
  responsible for maintaining the network (authorities) need to be
  known, rather than remain anonymous as in mining-based chains like
  Bitcoin and Ethereum.


It is underlined to use Proof-of-Authority for a private chain.

What is the reason? And Is it logical to use "Proof-of-Authority" for a "public" blockchain, in sense of keeping decentralization?
What is the reason? And Is it logical to use "Proof-of-Authority" for a "public" blockchain, in sense of keeping decentralization?


Proof of Authority is, by definition, centralised. If the authority nodes go rogue, or fail to reach consensus, the network is useless. 

You could use it in public networks (some of the ethereum testnets are PoA), but it would not be a decentralized network. The value of a PoA mainnet would have to come from some benefit of its centralization, and a very high level of trust in the trusted authorities.