In addition to the standards suggested for all Wikipedia articles, special attention to the following while expanding logic articles:
Guidelines for Philosophy articles
Guidelines for Mathematics articles
These standards, as with all featured article status should comply with these standards.
Note that new standards should be subjected to consensus building before being added here (a consensus should be reached on the discussion page).
Standard
For consistency use the following preferred symbols and terminology in Logic articles
It is useful to have an agreed set of symbols and terminology. 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
Symbols
For consistency use the following preferred symbols in Logic articles:
Truth Functional Connectives
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

$\exists$x or $\exists x$

$\exists x$

{{exist}}

\exists x

Terminology
For consistency use the following terminology in Logic articles:
Drafting in progress drafted cf Wikipedia talk:WikiProject Logic/Standards for notation#Terminology
It's good to talk (and a common language can only help.)
Common basis for syntax and semantics
One can talk about syntax while ignoring any possible semantics, or talk about semantics while ignoring that there might be a language describing them. The terms in the following table are common to both aspects.
Terminology used

Preferred terminology

Preferred meaning

signature

signature

a set of nonlogical symbols with specified arities

nonlogical symbol, nonlogical constant

nonlogical symbol

any of the symbols below

function letter (arity >0), operation letter/symbol (arity >0), function symbol (arity ≥0), function symbol (arity >0)

function symbol

either arity >0, i.e. excl. constant symbols, or arity ≥0, i.e. including constant symbols

individual constant, constant, (individual) constant symbol, constant symbol

constant symbol


predicate letter (arity >0), predicate symbol (arity ≥0), relation symbol (arity >0)

predicate symbol or relation symbol

either arity >0, i.e. excl. symbols below or arity ≥0, i.e. including symbols below

propositional variable, propositional letter, propositional symbol, sentential variable, sentential letter, sentential symbol

in propositional/sentential logic: prop./sent. variable in firstorder logic: nullary predicate/relation symbol


Note: Nullary function symbols are constant symbols, and nullary predicate/relation symbols are propositional/sentential symbols. What differs about firstorder logic between authors is 1) whether constant symbols are called (nullary) function symbols, and 2) whether proposition symbols are even allowed.
Syntax
The terms in the following table are used when working with syntax and are only marginally related to semantics.
Terminology used

Preferred Terminology

logical connective, connective, logical operator, propositional operator, truthfunctional connective, logical connective symbol


language, formal language, artificial language


sentence, statement, proposition (all when meaning a sentence in a formal language)


truthbearer


wellformed formula, wff, formula


Semantics
The terms in the following table relate to semantics; they are not needed when discussing only syntax, although of course they motivate the syntax.
Terminology used

Preferred Terminology

domain, domain of discourse, universe of discourse, universe, carrier, underlying set


extension, denotation


structure


function, operator


property, attribute, relation (arity=1)


property (arity>1), relation (arity>1)


Relation between syntax and semantics
Terminology used

Preferred Terminology

model


interpretation


Unsorted
Terminology used

Preferred Terminology

propositional logic, sentential logic, propositional calculus, sentential calculus, statement logic, statement calculus

propositional logic

firstorder predicate logic, firstorder logic, predicate logic,


argument, input


value, output


formal system, logical system, logistic system, logical calculus, logic


formal logic, mathematical logic, symbolic logic


elementary logic


