Wikipedia:WikiProject Logic/Standards for notation

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For consistency use the following preferred symbols and terminology in Logic articles

It is useful to have an agreed set of symbols and terminolgy. Not only do symbols vary from author to author, but any symbol may be written in a variety of fonts which may or may not appear on various browsers. The aim is consistency and legibility

Contents

[edit] Symbols

For consistency use the following preferred symbols in Logic articles:

[edit] Truth Functional Connectives

Connective Name Symbol(s) Preferred Symbol(s) Template <math> See
Negation NOT ¬ or ¬ or ~ ¬ {{not}} \neg Logical negation
Conjunction AND \wedge or & & {{and}} & Logical conjunction
Inclusive disjunction OR \vee \lor {{or-}} \vee Logical disjunction
Material implication IMPLIES \rightarrow or \Rightarrow or \supset or \to \to {{imp}} \rightarrow Material conditional
Material equivalence (biconditional) EQV or XNOR \leftrightarrow or \Leftrightarrow or = \leftrightarrow {{eqv}} \leftrightarrow Logical biconditional
Identity (definition) IS \equiv or := or = \equiv {{ident}} \equiv Law of identity
Neither-nor (joint denial) NOR or  ↓  {{nor-}} \downarrow Logical NOR
Not both (alternative denial) NAND {{nand}} \uparrow Alternative denial (nand)
Exclusive disjunction XOR \nleftrightarrow or + or \oplus or \nleftrightarrow {{xor}} \nleftrightarrow XOR

[edit] Quantifiers

Quantifier Description Symbols Preferred Symbol Template <math>
Universal For every x (x) or \forall x or  \forall x  \forall x {{all}} \forall x
Existential There exists an x \existsx or   \exists x   \exists x {{exist}} \exists x

[edit] Metalogical Symbols

Name Description/Usage Symbol(s) Preferred Symbol(s) Template <math> See
Theorem  X \vdash Y , \vdash Z , A \vdash_S X \vdash \vdash {{tee}} \vdash Turnstile (symbol)
Semantic Entailment, Logical Implication A \models_L X, \models X \models \models {{models}} \models Logical implication
True, tautology  \vDash \top \top or T or 1 \top {{true}} \top Tautology (logic)
False, contradiction  \vDash \neg\bot \bot or F or 0 \bot {{false}} \bot Logical value

[edit] Terminolgy

For consistency use the following terminology in Logic articles: To be drafted