Model (FOL)
From Maths
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Definition
For a given first order language, [ilmath]\mathscr{L} [/ilmath], with a structure, [ilmath]\mathbf{M} [/ilmath] and an assignment, [ilmath]\sigma[/ilmath], a 2-tuple (or ordered pair) [ilmath](\mathbf{M},\sigma)[/ilmath] is a model of [ilmath]\mathscr{L} [/ilmath][1].
- Fully expanded a model is a tuple, [ilmath]\underbrace{(\overbrace{(\underbrace{(M,\mathcal{F},\mathcal{R})}_{\text{Domain: }\mathbb{M} },\overbrace{I:\mathscr{L}\rightarrow \underbrace{(M,\mathcal{F},\mathcal{R})}_{\mathbb{M} } }^\text{Interpretation})}^\text{Structure},\underbrace{\sigma:V\rightarrow M}_\text{Assignment})}_\text{Model}[/ilmath]
