Information about individuals or groups of individuals might be selectively available to other individuals (or groups). For example, in a work setting, a colleague might know information about an individual’s work process; the manager might know additional details about the individuals work but might not know about their compensation; the HR, on the other hand, might not know much about the details of this person’s work-profile but might know the compensation details of this individual.
How some agents might gain access to information or other individuals has been discussed in the research paper by Alexandru Baltag and Sonja Smets titled “Learning What Others Know”, which forms the basis of the below text.
Importance of this research
Gaining access to data using information bits from multiple channels can be very useful in specific cases. For example, suppose Google, Amazon, or Netflix could find a way to share information about some particular person. In that case, the resulting recommendation system could profile users of their services accurately and show recommendations to this person of things before they know they need them. Quite understandable, the risk of the information falling into unsolicited hands also exists.
Contribution of the research paper
- Background on epistemic logic is provided in the paper.
- Epistemic comparative assertions for groups are presented, and the axiomatization of the resulting logic is shared.
- Public and semi-public sharing/reading actions are presented and are axiomatized in the absence of common knowledge operators.
- Motivated by the problems posed by common knowledge, the notion is generalized (to “common distributed knowledge”).
- A complete and decidable axiom system is presented, and it is also used to axiomatize semi-public actions.
- Arbitrary reading actions are further generalized.
- Conjecture is identified as the future scope of work.
How can information be transferred?
The agent could have got access to information in multiple ways. For example, let us consider two agents, A & B. Possible case scenarios are as below:
- A might grant access to B to view A’s information.
- B might gain access to A’sA’s information illegally (Example Hacking), but the fact that A has access is not in the public domain.
- B might gain access to A’sA’s information illegally, but the fact that A has gained information is public.
Types of information access
- Public: Everyone knows that the information is available for all
- Semi-public: When access is with specific individuals & everyone knows who all have the access
- Private: Both the information and the access are unknown to outsiders
Conclusion
The researchers have presented an in-depth analysis of information sharing between different agents in this research paper. The researchers have also used mathematical models to represent possible data sharing or data leak scenarios. In the words of the researchers,
We should stress that the completeness and decidability results in this paper are non-trivial: we are not aware of any known decidable logic in which our logic can be embedded via some obvious translation. All-natural candidates (e.g. the known decidable extensions of mu-calculus or of Propositional Dynamic Logic, the fixed-point extensions of the guarded fragments of First-Order Logic, Monadic Second-Order Logic etc.) seem to be able to embed only some proper fragment of our logics. Indeed, the logic presented in this paper are so powerful that they seem to come very close to the borderline where expressivity runs into undecidability.
Source: Alexandru Baltag and Sonja Smets “Learning What Others Know“
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