Part 2. Semantic Validity Proofs

For each of the problems in this section, prove through ordinary reasoning that the argument from the premises to the conclusion is valid. To do this you will need to express, in ordinary language, how in a model in which each of the premises is true, the conclusion must be true. Alternatively you may express, in ordinary language, how in a model in which each of the premises is true, the conclusion cannot be false. Or, if you so choose, you may show that it is impossible to construct a model in which the conclusion is false if all the premises are true by showing that, on the assumption that such a model exists, there is some contradiction (e.g. some object in the model both has and also does not have some property). Note: all domains have some element in them.

Symbols to use for cutting and pasting if needed:

2.03)

Premises: ( x Ox ) (x Px), x Ox, x (Mx Px)

Conclusion: x ( Mx Hx)