Here are the syllogistic figures identified by Aristotle and his successors, along with their medieval names:
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Barbara. All G are F. All H are G. So: All H are F
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Celarent. No G are F. All H are G. So: No H are F
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Ferio. No G are F. Some H is G. So: Some H is not F
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Darii. All G are H. Some H is G. So: Some H is F.
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Camestres. All F are G. No H are G. So: No H are F.
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Cesare. No F are G. All H are G. So: No H are F.
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Baroko. All F are G. Some H is not G. So: Some H is not F.
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Festino. No F are G. Some H are G. So: Some H is not F.
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Datisi. All G are F. Some G is H. So: Some H is F.
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Disamis. Some G is F. All G are H. So: Some H is F.
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Ferison. No G are F. Some G is H. So: Some H is not F.
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Bokardo. Some G is not F. All G are H. So: Some H is not F.
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Camenes. All F are G. No G are H So: No H is F.
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Dimaris. Some F is G. All G are H. So: Some H is F.
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Fresison. No F are G. Some G is H. So: Some H is not F.
Symbolize each argument in FOL.
Magnus et al., forall x: Calgary, First-order logic, Sentences with one quantifier, Exercise A