Difference between revisions of "Interpretation (FOL)"

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==References==
 
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{{Definition|Formal Logic}}
 
{{Definition|Formal Logic}}

Latest revision as of 06:54, 10 September 2016

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Created so I don't have to sift through notes or scour PDFs, it needs more references and fleshing out

Definition

An interpretation is a mapping, I:LM 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:LM instead. Recall a domain is a 3-tuple, (M,F,R). An interpretation has the following properties[1]:

  1. For each constant symbol, c in L, I(c) is an element of M
  2. For each n-ary function symbol, f in L, I(c) is an element of F
  3. 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

See next

References

  1. Jump up to: 1.0 1.1 Mathematical Logic - Foundations for Information Science - Wei Li

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