In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols (sometimes also called logical and non-logical constants). The logical constants, by contrast, have the same meaning in all interpretations. They include the symbols for truth-functional connectives (such as "and", "or", "not", "implies", and logical equivalence) and the symbols for the quantifiers "for all" and "there exists".
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| - Simbolo non logico (it)
- Non-logical symbol (en)
- Símbolo não lógico (pt)
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| - In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols (sometimes also called logical and non-logical constants). The logical constants, by contrast, have the same meaning in all interpretations. They include the symbols for truth-functional connectives (such as "and", "or", "not", "implies", and logical equivalence) and the symbols for the quantifiers "for all" and "there exists". (en)
- O conjunto dos símbolos não lógicos (pré-AO 1990: símbolos não-lógicos) é a parte de uma linguagem de primeira ordem que informa a sua “área de especialidade” (além da expressividade geral). Uma ideia análoga pode ser vista na distinção entre e os axiomas “próprios”, “profissionais” da teoria específica que se está axiomatizando ou investigando. (pt)
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| - In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols (sometimes also called logical and non-logical constants). The non-logical symbols of a language of first-order logic consist of predicates and individual constants. These include symbols that, in an interpretation, may stand for individual constants, variables, functions, or predicates. A language of first-order logic is a formal language over the alphabet consisting of its non-logical symbols and its logical symbols. The latter include logical connectives, quantifiers, and variables that stand for statements. A non-logical symbol only has meaning or semantic content when one is assigned to it by means of an interpretation. Consequently, a sentence containing a non-logical symbol lacks meaning except under an interpretation, so a sentence is said to be true or false under an interpretation. These concepts are defined and discussed in the article on first-order logic, and in particular the section on syntax. The logical constants, by contrast, have the same meaning in all interpretations. They include the symbols for truth-functional connectives (such as "and", "or", "not", "implies", and logical equivalence) and the symbols for the quantifiers "for all" and "there exists". The equality symbol is sometimes treated as a non-logical symbol and sometimes treated as a symbol of logic. If it is treated as a logical symbol, then any interpretation will be required to interpret the equality sign using true equality; if interpreted as a non-logical symbol, it may be interpreted by an arbitrary equivalence relation. (en)
- O conjunto dos símbolos não lógicos (pré-AO 1990: símbolos não-lógicos) é a parte de uma linguagem de primeira ordem que informa a sua “área de especialidade” (além da expressividade geral). Uma ideia análoga pode ser vista na distinção entre e os axiomas “próprios”, “profissionais” da teoria específica que se está axiomatizando ou investigando. Os símbolos não-lógicos são estruturados de acordo com a assinatura adotada. Eles são os símbolos de função e os símbolos de relação (predicados) dessa assinatura e cada um deles (seja símbolo de relação ou de função) tem uma aridade. As constantes, por serem funções 0-árias, são também símbolos não-lógicos. (pt)
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