List questions from propositional-calculus

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Is the negation of "p iff q", "(not p) iff q"?

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Implication arrows, turnstiles etc

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Questions about proving $\lnot \lnot a = a$

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Rewrite each of the following sentences using logical connectives

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If $A \vdash a$ and $B \vdash b$ then $A \cup B \vdash a$ and $A \cup B \vdash b$? Question about the empty set and axioms.

Published on 09 Apr 2026 - 5:31

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Checking for validity using truth table (shortcut)

Published on 12 Apr 2026 - 13:39

203

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How can we prove soundness property if it's possible for our assumption set to contain false assumptions?

Published on 04 May 2026 - 20:30

166

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Adding Łukasiewicz-style quantifiers over truth value (Σ, Π) to classical sentential logic

Published on 14 Apr 2026 - 5:13

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meaning of (r .⊃. s ⊃ r) [the syntax meaning]

Published on 12 Apr 2026 - 10:05

453

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Proving soundness property of a Hilbert system

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236

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What does semantic entailment even mean, in the context of completeness?

Published on 05 May 2026 - 1:53

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Converse of substitution for propositional letters

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Does natural deduction require a non-empty set of premises?

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Prove the logical equivalence $(p \land (q \lor (r ∧ \lnot s) \to v)) ∨ p \equiv p$

Published on 15 Apr 2026 - 12:38

List Question

In the deduction theorem, what exactly is contained in $\Delta$?

Is the negation of "p iff q", "(not p) iff q"?

Implication arrows, turnstiles etc

Questions about proving $\lnot \lnot a = a$

Rewrite each of the following sentences using logical connectives

If $A \vdash a$ and $B \vdash b$ then $A \cup B \vdash a$ and $A \cup B \vdash b$? Question about the empty set and axioms.

Checking for validity using truth table (shortcut)

How can we prove soundness property if it's possible for our assumption set to contain false assumptions?

Adding Łukasiewicz-style quantifiers over truth value (Σ, Π) to classical sentential logic

meaning of (r .⊃. s ⊃ r) [the syntax meaning]

Proving soundness property of a Hilbert system

What does semantic entailment even mean, in the context of completeness?

Converse of substitution for propositional letters

Does natural deduction require a non-empty set of premises?

Prove the logical equivalence $(p \land (q \lor (r ∧ \lnot s) \to v)) ∨ p \equiv p$

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