Wikipedia:WikiProject Logic/Standards for notation: Difference between revisions

Revision as of 23:24, 1 April 2009

Revision as of 14:21, 8 April 2009

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'''It's good to talk (and a common language can only help.)'''

</blockquote>

===Common basis for syntax and semantics===

{| class="wikitable"

|-

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! Preferred Terminology

|-

|logicalpropositional connectivevariable, connective,propositional logical operatorletter, propositional operatorsymbol, truth-functionalsentential connectivevariable, logicalsentential connectiveletter, sentential symbol

|

|-

|Non-logical symbol, non-logical constant

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

|

|-

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

|first-order predicate logic, first-order logic, predicate logic,

|

|-

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

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

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|-

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

|Non-logical symbol, non-logical constant

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|-

|signature

|___domain, ___domain of disourse, universe of discourse, universe, carrier, underlying set

|

|}

===Syntax===

{| class="wikitable"

|-

! Terminology used

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

! Preferred Terminology

|

|-

|logical connective, connective, logical operator, propositional operator, truth-functional connective, logical connective symbol

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

|

|-

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

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

|

|-

|language, formal language, artificial language

|[[extension]], [[denotation]]

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|-

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

|intepretation

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|-

|[[truthbearer]]

|model

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|-

|well-formed formula, wff, formula

|signature

|

|}

===Semantics===

{| class="wikitable"

|-

! Terminology used

|structure

! Preferred Terminology

|

|-

|___domain, ___domain of disoursediscourse, universe of discourse, universe, carrier, underlying set

|language, formal language, artificial language

|

|-

|[[extension]], [[denotation]]

|argument, input

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|-

|structure

|value, output

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|-

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|[[Property (philosophy)|property]] (arity>1), relation (arity>1)

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|}

===Relation between syntax and semantics===

{| class="wikitable"

|-

! Terminology used

|[[formal system]], logical system, logistic system, logical calculus, logic

! Preferred Terminology

|-

|model

|

|-

|interpretation

|formal logic, mathematical logic, symbolic logic

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|}

===Unsorted===

{| class="wikitable"

|-

! Terminology used

|elementary logic

! Preferred Terminology

|-

|first-order predicate logic, first-order logic, predicate logic,

|

|-

|argument, input

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

|

|-

|value, output

|[[truthbearer]]

|

|-

|[[formal system]], logical system, logistic system, logical calculus, logic

|well-formed formula, wff, formula

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|-

|formal logic, mathematical logic, symbolic logic

|

|

|-

|elementary logic

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|}