Deducing the semantics of a sentence and write it in set format.

Question

This is a question from semantics in linguistics. The semantics of a statement are written in set format eg.

Sentence: John caught a fish.

[John] = {x:x E J} ; J is the set of all individuals named John

[fish] = {y:y E F} ; F is the set of all objects called Fish

[caught] = Set of ordered pairs of objects <x, y> s. t. caught y = [<x, y> : x caught y]

[caught a fish] = C ; Set of individuals who caught a fish = {x: <x, y> E [<x, y> : x caught y and y E F]}

[[John caught a fish]] = 1 iff John E C = {x : <x, y> E [<x. y> : x caught y, y E F]}

What will the semantics for the statement: John caught a fish and sold it to Bill. ?

Answer 1

[John] = {x: x E J} ; J is the set of all individuals named John

[Bill] = {y: y E B} ; B is the set of all individuals named Bill

[fish] = {z: z E F} ; F is the set of all objects called Fish

[caught] = {<x,z>: x caught z} ; Set of ordered pairs where x caught z

[sold] = {<x,y,z>: x sold z to y} ; Set of ordered triples where x sold z to y

[it] = {z: <x,z> E [caught]} ; The fish that John caught

[[John caught a fish and sold it to Bill]] = 1 iff

∃z( <John,z> E [caught] ∧ <John,Bill,z> E [sold] )

Words:

There exists a fish z that was caught by John and sold by John to Bill.