Source: p 145. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko.
"Buffalo" sentences (pp. 73, 101, and 139) can be formalized if we establish two conventions. First, that the noun "buffalo" should be interpreted as "all buffalo" (or "all bison"). Second, if there is no object to the verb "buffalo", then we interpret it as "buffalo some buffalo" (or "intimidate some bison"). So "Buffalo buffalo" is "All bison intimidate some bison". Let Bx mean that x is a buffalo (or bison). Let Ixy mean that x buffalos (or intimidates) y. Then we can express "Buffalo buffalo" as ∀x ( Bx ⟹ ∃y(By ∧ Ixy) ).
- Formalize "Buffalo buffalo buffalo buffalo buffalo" where we mean "All bison intimidate all bison, that all bison intimidate".
[ p 360 : ] 17. ∀x ( Bx ⟹ ∀y ( ( By ∧ ∀z (Bz ⟹ Izx) ) ⟹ Ixy) )
The following was my attempt; I added colour and changed the brackets to ease reading.
Why should the red y instead be x (per the above answer)? I wrote the red y because the green restrictive relative clause modifies bison2, and not bison1.