# What logic(s) exist for attributing belief?

I'm looking for an appropriate formalism to represent "traceability" in claims, especially connecting conclusions to source materials in a rigorous way. For example, I'd like to be able to represent something like the following chain of thoughts (Assume "I" is well-defined here):

• Consider document X (stored in some format).
• I believe that X corresponded to the URL https://www.iaea.org/sites/default/files/gov2010-46.pdf as of 10/24/2017, because I downloaded it from there on that date.
• I believe that the text "Implementation of the NPT Safeguards Agreement and relevant provisions of Security Council resolutions in the Islamic Republic of Iran" occurs at position Y in the file, because Adobe Acrobat extracted it.
• I believe that those words are the title of the document, because I looked at it and I say so.
• I believe that the text "3 On 28 August 2010, of the 8856 centrifuges which had been installed at FEP, 3772 centrifuges were being fed with UF6." appears in the document at position Z, because Adobe Acrobat extracted it.
• I believe that text is "Footnote 3 of paragraph 4 in section A.1" because I looked at it and I say so.
• I believe that Document X is asserting this statement to be true, because of my human judgment of the context.
• I believe that "On August 28 2010 there were 8856 centrifuges installed at FEP" is equivalent to or implied by that statement, because of my human interpretation of those words"
• I believe that, in that text, "FEP" means "The Fuel Enrichment Plant at Natanz" because of human judgment of the context.
• I believe that Formula FOO represents the english-language statement "On August 28 2010 there were 8856 centrifuges installed at the Fuel Enrichment Plant at Natanz" because I wrote it and assert that it's an accurate encoding.
• I believe that document X was written by "The Director General of the IAEA" because ___ .
• I believe that document X is dated "6 September 2010" because ___ .
• I believe that "'The Director General of the IAEA' asserts what X asserts, as of 9/6/2010" by inference from the previous 2 statements.
• I believe that "As of 9/6/2010, 'The Director General of the IAEA' asserts FOO", by inference from the preceding statements a,b, and c.

It would additionally be nice to represent derivations like:

• I believe that "As of 9/6/2010 FOO" because I trust 'The Director General of the IAEA' (possibly in some limited scope).

At this point, I'm not yet looking at complete reasoning over such a chain of attribution, though of course that's a desirable end state. Right now, I'd like to be able to do more ad-hoc queries like "Person B does not trust the Director General, should B believe FOO" -- to which the answer would be no, given only the evidence we've shown here. Depending on the object language in which I we wrote FOO, it would be nice to be able to say "Bob should still believe Formulas BAR and BAZ for other reasons; those imply FOO or imply something close to FOO."

After all that -- does anyone know of formalisms that can capture this sort of epistemic assertions? Double bonus if it's somewhat tractable to reason over. I've so far assumed that "the logic for beliefs" and "the logic for the word" are unrelated, but if a single logic can capture both, that's even better.

• To clarify, how much do you already know about modal logic? – Bjørn Kjos-Hanssen Oct 24 '17 at 22:40
• This question has been extensively and inconclusively studied by epistomologists for over 50 years. Right now, this question is doubly off topic: for one it is too broad for this site and for two even if it were constrained it would be off topic because it's not about computer science. – Stella Biderman Oct 25 '17 at 18:32
• @BjørnKjos-Hanssen, let's go with "I know what it is, but I'm not deeply conversant." My logic background mostly comes from the programming languages side, with a little bit of design verification and security. I'm familiar with trust logics like Delegation Logic, but those only get one a little bit of the way here (at least as I understand the problem). – Eric Anderson Oct 26 '17 at 20:44
• @StellaBiderman, I'll take the "too broad," but there's no way this isn't computer science. It's also mathematics and philosophy, but those are highly overlapping areas when it comes to logic, reasoning, knowledge representation, etc. – Eric Anderson Oct 26 '17 at 20:47
• Did you try looking at Joe Halpern's works. Specifically, this one sounds relevant: cs.cornell.edu/home/halpern/abstract.html#journal61 – Guy Oct 29 '17 at 6:46