Talk:Truth table

Applications

"This demonstrates the fact that p ⇒ q {\displaystyle p\Rightarrow q} p\Rightarrow q is logically equivalent to ¬ p ∨ q {\displaystyle \lnot p\lor q} {\displaystyle \lnot p\lor q}." Then, logically, isn't one of these functions redundant and therefore completely unnecessary? — Preceding unsigned comment added by 2601:602:780:3926:9526:680D:B40F:658F (talk) 00:10, 25 June 2019 (UTC)

Dual typo

It appears Verum ⊤ ought to be the dual of Falsum ⊥ —OK? --Ancheta Wis   (talk | contribs) 06:22, 3 July 2020 (UTC)

p	q		F0	NOR1	↚2	¬p3	↛4	¬q5	XOR6	NAND7		AND8	XNOR9	q10	→11	p12	←13	OR14	T15
Dual			T15	NAND7	→11	¬p3	←13	¬q5	XNOR9	NOR1		OR14	XOR6	q10	↚2	p12	→11	AND8	F0

If you mean De Morgan duality, yes, that is right. You get the De Morgan dual by negating each operand and also the operator: for a constant that is just negating the constant. Glancing over the article didn't reveal what part in particular you are interested in. — Charles Stewart (talk) 06:40, 3 July 2020 (UTC)

Thank you. I adjusted the typo.

Another question: perhaps Adj deserves a sentence. Might Adj mean 'adjoint' in the Adj row for 'Truth table for all binary logical operators' ? Adjoint is a dab listing. --Ancheta Wis   (talk | contribs) 14:56, 4 July 2020 (UTC)

Implication is associative

Implies *is* associative. 𝑝→(𝑞→𝑟) should not be read as "p implies that q implies p, but "p implies q which implies r"

The reason why the brackets rule does not work is because of notational peculiarities. Associativity is not about brackets, associativity is about successive applications of an operator, which is different. And the successive applications of the implies operator yield same result independent of the order in which the operations are performed.

Read about https://en.wikipedia.org/wiki/Light%27s_associativity_test — Preceding unsigned comment added by 94.26.72.172 (talk) 17:49, 31 March 2021 (UTC)

Size of truth table

Better naming would be ‘number of truth tables’ (for given n; the size of a truth table for n bits is 2^n) — Preceding unsigned comment added by 178.83.38.187 (talk) 15:37, 27 June 2022 (UTC)

Truth tables outside of classical logics

I'd like to have some text in the article about truth tables outside of classical logics. My first attempt ("they mostly can't be used there") was reverted by David Eppstein with a link to Sylvan.1992 which turned out to be based on Tennant.1989, a more elaborate paper. For a second attempt, I'd suggest a text like

Tenant gives a proof-theoretic investigation of truth tables in both classical and nonclassical logics, based on a strict "left-right reading" that does not require each formula to have a truth value in the set {T,F}. See also Three-valued logic#Logics and Four-valued logic#Logical connectives for examples of truth-tables in logics with >2 truth values.

However, I'm not sure I understood the papers correctly, so I'd like to have some advice from a proof theory expert.

As an aside, Tenant explains on p.460, truth value assignments need not be total functions, while on p.462, he claims that after taking care of redundancies, the disjunction truth table says if the truth value of A is T then that of (A or B) is T; the latter conclusion can be drawn (from an ordinary 4-row table as shown on p.463) only if the truth value of B is assumed (to be defined and) in the set {T,F}. - Jochen Burghardt (talk) 14:43, 22 May 2024 (UTC)

References