View source for Semantics of terms (FOL)

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==Definition==
Given a [[first order language]], {{M|\mathscr{L} }} and a {{link|model|FOL}}, {{M|(\mathbf{M},\sigma)}} of {{M|\mathscr{L} }} also, the {{link|semantics|FOL}} of a {{link|term|FOL}}, {{M|t\in\mathscr{L}_T}}, which we denote by {{M|t_{\mathbf{M}[\sigma]} }} is [[inductive definition|defined inductively]] as follows{{rMLFFISWL}}:
# If {{M|x}} is a {{link|variable symbol|FOL}} then: {{M|1=x_{\mathbf{M}[\sigma]}:=\sigma(x)}}
# If {{M|c}} is a {{link|constant symbol|FOL}} then: {{M|1=c_{\mathbf{M}[\sigma]}:=c_\mathbf{M} }} (recall {{M|c_\mathbf{M} }} denotes {{M|I(c)}} where {{M|I}} is an {{link|interpretation|FOL}})
# If {{M|f}} is an ''[[arity|{{n|ary}}]]'' {{link|function symbol|FOL}} and {{M|t_1,\ldots,t_n\in\mathscr{L}_T}} are {{link|term|FOL|s}} then: {{M|1=(ft_1\cdots t_n)_{\mathbf{M}[\sigma]}:=f_\mathbf{M}((t_1)_{\mathbf{M}[\sigma]},\ldots,(t_n)_{\mathbf{M}[\sigma]})}} (recall {{M|f_\mathbf{M} }} denotes {{M|I(f)}} where {{M|I}} is an {{link|interpretation|FOL}})

==See next==
* {{Link|Semantics of logical connectives|FOL}}
** {{link|Semantics of formulas|FOL}}
==References==
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