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Advanced Logic Analysis: Critical Theorems Unraveled

Dive into complex logic theorems, unravel critical propositions, and explore discharges in logical assumptions. Analyze undischarged assumptions and their implications with detailed examples.

erica-king
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Advanced Logic Analysis: Critical Theorems Unraveled

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  1. I • P(a/x) • xP • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q. • I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • E • xP • P(a/x)

  2. I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • Fa Assumption • xFx 2 I

  3. I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • Fa Assumption • xFx 2 I • xFxx Assumption • Fbb 1 E • xFxb 2 I

  4. Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q.

  5. Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx

  6. Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx • xFx • Fa • Fa • Fa

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