query: How can we prove soundness property if it's possible for our assumption set to contain false assumptions?
positive_passages.docid: 147051
positive_passages.text: Soundness vs completeness, am I understanding? And proving soundness?
negative_passages.docid: 106799
negative_passages.text: Proof Verification: Converse of Intermediate Value Theorem
negative_passages.docid: 70585
negative_passages.text: Why does Assuming[x > 0, TrueQ[x > 0]] return False?
negative_passages.docid: 140241
negative_passages.text: Proving OLS unbiasedness without conditional zero error expectation?
negative_passages.docid: 126870
negative_passages.text: Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
negative_passages.docid: 94617
negative_passages.text: Showing Consistency and Completeness implies a unique truth assignment
negative_passages.docid: 61303
negative_passages.text: "Infer" vs. "imply" — can "infer" imply "imply"?
negative_passages.docid: 68607
negative_passages.text: Could an argument with false Premises and a true Conclusion be logically valid?
negative_passages.docid: 136734
negative_passages.text: Do truth tables need proofs?
negative_passages.docid: 72034
negative_passages.text: Truth table and the meaning of $\oplus$ in propositional logic
negative_passages.docid: 133194
negative_passages.text: Can we prove reality?
negative_passages.docid: 148239
negative_passages.text: natural deduction proof with De Morgan's laws
negative_passages.docid: 29629
negative_passages.text: Distinguishing between valid and fallacious arguments (propositional calculus)
negative_passages.docid: 73807
negative_passages.text: Prove positive definiteness
negative_passages.docid: 116527
negative_passages.text: Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
negative_passages.docid: 52322
negative_passages.text: Implication in mathematics - How can A imply B when A is False?
negative_passages.docid: 53101
negative_passages.text: Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?