Wikipedia:WikiProject Logic/Logical Operators

Proposal

A subproject of WikiProject Logic for the purpose of expanding, and integrating the articles describing the Logical Operators.

There are 16 binary logical operators. The concept behind each of them is applied in various disparate fields: (logic, mathematics, grammar, computer science, linguistics). Each of the sixteen has the potential to reach featured article status with time and effort.

I propose to see:

• A) the logical, grammatical, mathematic, and computer science applications all on the same page for the same concept with links to the main article for each section as appropriate.
• B) similar sections including truth table, venn diagram, properties (including theorems that demonstrate the properties), symbols (preferably from all the above disciplines).
• C) several merges including If and only if, logical biconditional, and logical equality; different pages for implication; logical NOR and NOR gate; others
• D) unifying main page and nav bar.

Project Map

Tautology	Nand	Material Implication	not p
$\top$ Tautology (logic) Tautology (rhetoric) True Truth Truth value	$\uparrow$ Nand NAND Gate Sheffer stroke Ampheck Sole sufficient operator	$\rightarrow$ Material implication Counterfactual conditional Indicative conditional Corresponding conditional (logic) Strict conditional Logical implication	$\neg p$ Negation Not! Negation (rhetoric)
Converse implication	not q	Material Equivilence	Joint Denial
$\leftarrow$ Converse implication Conversion (logic)	$\neg q$ Negation Not! Negation (rhetoric)	$\equiv$ Material equivalence If and only if Logical equivalence Logical equality XNOR gate Biconditional elimination Biconditional introduction	$\downarrow$ Joint denial Ampheck Bitwise NOR NOR gate Sole sufficient operator
Inclusive Disjunction	Exclusive Disjunction	q	Converse nonimplication
$\lor$ Logical disjunction And/or Bitwise OR Disjunction elimination Disjunction introduction OR gate	$\not \equiv$ Exclusive disjunction Bitwise XOR XOR gate Exclusive or	$q$ Law of Identity	$\not \leftarrow$ Converse nonimplication
p	Material Nonimplication	Conjunction	Contradiction
$p$ Law of Identity	$\not \rightarrow$ Material nonimplication	$\land$ Logical conjunction AND gate Binary and Bitwise AND Conjunction introduction Conjunction elimination Grammatical conjunction	$\bot$ Contradiction False