Propositional truth tables, Computer Engineering

Propositional truth tables:

There {X\t} is a substitution that replaces all occurances of variable X with a term representing an object t as: 

  • ∀X. A is true if and only if A.{X\t} for every one t in Δ
  • ?X. A is true if and only if A.{X\t} for at any rate one t in Δ

 

By repeating this for all the quantifiers than we get a set of ground formulae in which we have to check that if the original sentence is true or false. But unfortunately, we don't have specified there that our domain Δ is finite -  like in example we see that it may contain the natural numbers -  but there may be a infinite number of sentences to check for a given model! So there may be also be an infinite number of models. And although we have a proper definition of model hence a proper semantics for first-order logic and we can't rely on having a finite number of models like we did where drawing propositional truth tables.

Posted Date: 1/11/2013 5:59:37 AM | Location : United States







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