The Justification of Deduction

If someone comes to my house, saying, "Here is a bone; I hope Obrecht likes it," I might answer with a deductive argument: "You may rest assured on that score. Obrecht is a dog, and all dogs like bones; therefore Obrecht will like it." We may formalize this argument as follows: Let G be the bone, O be Obrecht, D be the class of dogs, B be the class of bones, and, finally, let L be the class of ordered pairs such that x likes y. The premises are then: x ∈ D ⋅ y ∈ B ⋅ ⊃ ∈ L) G ∈ B O ∈ D