Difference between revisions of "Interpretation (FOL)"
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Created so I don't have to sift through notes or scour PDFs, it needs more references and fleshing out
Contents
[hide]Definition
An interpretation is a mapping, I:L→M where L is a first order language and M is a domain[1]. As we often identify a domain with its set, we may write I:L→M instead. Recall a domain is a 3-tuple, (M,F,R). An interpretation has the following properties[1]:
- For each constant symbol, c in L, I(c) is an element of M
- For each n-ary function symbol, f in L, I(c) is an element of F
- For each n-ary predicate symbol, P in L, I(P) is an element of R
An interpretation is usually used as part of a structure (of a first order language, L), M, which is a 2-tuple: M:=(M,I) where M is a domain and I an interpretation as defined above. When an interpretation is used as a part of a structure we adopt the following notation:
- I(c) is written cM,
- I(f) is written fM and
- I(P) is written PM