# How can you intuit Information Implication with 4 Truth Values?

Source: p 158. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko.

[...] Call this Information Implication. Its truth table looks like this:

This question focuses on the 5 rows numbered in red above. I already understand how to conclude the Truth Values for ⟹; so please do not answer with formal proofs or Truth Tables.

My problem: they still feel counterintuitive. So can they be intuited or explained directly, without relying on the intermediate step (B → S) ≡ (¬B ∨ S)? For example, consider 8 and 12: how does it make intuitive sense for the Truth Value to differ from A's or B's?

• Why would you expect something this artificially constructed to be intuitive? – jobermark Aug 10 '16 at 20:33
• @jobermark This is artificially constructed, but was constructed to expand on (and maintain) the normal 2-valued Material Implication. So all the possibilities with A = 0 or 1 are intuitive to me, because of the Principle of Explosion when A = 0. – Greek - Area 51 Proposal Aug 11 '16 at 3:29