Logic

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WFFS:

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Freedom
An occurrence of a variable v is free iff v does not occur
set of all
grammatical expressions of fol, including both
incomplete claims, like ‘Tet(x)’ and complete ones

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Sentences

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formulas that make complete claims;
contain no variables or only bound ones

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Satisfaction occurs when:

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we give a o a name that’s not taken, call it ni , then S(ni) is true
S(ni ) is the result of replacing every occurrence of x in S(x) with ni

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4 Aristotelian Forms:

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All A's are B's: ∀x (A(x) → B(x))
Some A's are B's: ∃x (A(x) ∧ B(x))
No A's are B's: ¬∃x (A(x) ∧ B(x))
Some A's are not B's: ∃x (A(x) ∧ ¬B(x))

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FOL validity:

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impossible to be false if meanings of symbols are true

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prenex form

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When all of a formula’s quantifiers are stacked up in front of the formula

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universal elimination

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From ∀x S(x) you may infer S(c)

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existential introduction

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From S(c) you may infer
∃x S(x)

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existential elimination

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Given ∃x S(x), you may give a dummy name to (one of) the ob ject(s) satisfying S(x), say c, and then assume S(c)

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universal introduction

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Introduce a new name c to stand for a completely arbitrary member of the domain of discourse
prove c conclude all c