Definition:Language of Predicate Logic/Formal Grammar/Term
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This page is about Term in the context of Predicate Logic. For other uses, see Term.
Definition
Part of specifying the language of predicate logic $\LL_1$ is the introduction of terms.
The terms of $\LL_1$ are identified by the following bottom-up grammar:
\((\mathbf T \ \textrm {VAR})\) | $:$ | A variable of $\LL_1$ is a term | |||||||
\((\mathbf T \ \FF_n)\) | $:$ | Given an $n$-ary function symbol $f \in \FF_n$ and terms $\tau_1, \ldots, \tau_n$:
is also a term. |
Colloquially, we can think of a term as an expression signifying an object.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): term: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): term: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): term: 2.
- 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.5$ First-Order Logic Syntax: Definition $\mathrm{II}.5.3$