Difference between Term, Proposition and Formula

Master / Vertiefung Künstliche Intelligenz
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Difference between Term, Proposition and Formula
Is the following correct about the difference between Terms, Propositions and Formulae in PL1? (I am following the definitions 13.2.3 and 13.2.4 of 2019/2020)

  1. A Term is either one single variable, or a function applied to n Terms. (–> recursive definition)

  2. A Proposition is anything that is not a Term. So it can be a predicate, truth literal, two Terms connected using one of the known connectives, … So, a Proposition may consist of Propositions and Terms. But a Term may not contain a Proposition.

  3. A formula is either a Proposition (–> complex formula), or a Term (–> atomic formula).

Is this correct, or am I missing something? I am especially asking because of Assignment 6.4, where we make a distinction between “formula” and “term”.

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Often formula and proposition are synonyms.

But indeed the notes sometimes imply that anything can be called a formula, e.g., either a term or a proposition.

In any case, in A6.4, there are terms on the one hand (your case 1) and propositions/formulas on the other hand (your case 2).

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OK, thank you! :slight_smile: