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then it follows logically that:
:''All mice are afraid of at least one cat''.
The syntax of [[traditional logic]] (TL) permits exactly one quantifier, i.e. there are four sentence types: "All AsA's are BsB's", "No AsA's are BsB's", "Some AsA's are BsB's" and "Some AsA's are not BsB's". Each type is a quantified sentence containing exactly one quantifier. Since the sentences above each contain two quantifiers ('some' and 'every' in the first sentence and 'all' and 'at least one' in the second sentence), they cannot be adequately represented in TL. The best TL can do is to incorporate the second quantifier from each sentence into the second term, thus rendering the artificial-sounding terms 'feared-by-every-mouse' and 'afraid-of-at-least-one-cat'. This in effect "buries" these quantifiers, which are essential to the inference's validity, within the hyphenated terms. Hence the sentence "Some cat is feared by every mouse" is allotted the same [[logical form]] as the sentence "Some cat is hungry". And so the logical form in TL is:
