# Are there any logics to formalize understanding?

Are there any logics (modal-based or others) to formalize the following statement:

"agent A understands p". For example "agent A understands that Titanic sank because it hit an iceberg"

Where "understands" could be considered as a modal operator like the epistemic modal operator "agent A knows p".

Thank you,

• When I looked into logics for cryptographic protocols, I encountered two separate, versions of knowledge: "knowing a message" and "knowing that what a message claims is true". Is this the type of distinction you are trying to look into? If not, then it would help if you clarified a bit more on how your "understands" operator differs from a "knows" operator. – mdxn Dec 21 '14 at 20:39
• Perhaps justification logic? link – Luka Mikec Dec 22 '14 at 0:30
• In the context of distributed systems, Joseph Y. Halpern has studied "reasoning about knowledge and uncertainty". However, for more specific answers, it would be better to clarify how "understands" differs from "knows", as indicated by @mdx . For example, are there some axioms on "knows" that "understands" does (or should, in your context) not satisfy? – hengxin Dec 22 '14 at 9:00
• @mdx: Maybe the question conveys some confusion. When I reefed to the epistemic modal operator "know" I was referring to "knowing a message" as you've said. The difference is that I'm looking for a logic that can model the following attitude: "agent A understands that Titanic sank because it hit an iceberg". – user30441 Dec 22 '14 at 10:43
• @LukaMikec and mdx, I'll try to reformulate your comments so that I can be sure I get the point, please correct me if I'm wrong. By using justification logic you mean "A understands p" iff "A has (or can generate) a proof (justification) of p" ? What do you think of the following formalization by means of the epistemic operator "know": "A understands p" iff "A knows a proof (justification) of p" ? – user30441 Dec 22 '14 at 15:33