Logical Entailment

Created on March 6, 2013, 3:01 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:35 p.m.

In Logical Entailment a Theory is a Set of Formulas. Therefore a Theory is pretty much the same as a Knowledge Base. Then an Interpretation I is a model of T, only then if for all formulas G and T, I is a Model. A Formula F is a Consequence T only then if all models of T are also Models of F, then we can write T entails F and F is logical Consequence of the knowledge base T. On the other hand we know this already know the two formulas F and G are also in First Order Logic logical equivalent, if and only if G is a consequence of F and F is a Consequence of G. Then we can state F is equivalent to G.

  • a theory is a set of Formulas.
  • an Interpretation I is a Model of T. if I ⊨ G for all formulas G in T
  • a formula F is a logical Consequence of T, if all Models of T are also Models of F.
  • Then we write T ⊨ F.
  • Two Formulas F, G are called logical Equivalent, if {F} ⊨ G and {G} ⊨ F.
  • then we write F ≡ G

TheoryKnowledge Base

Construct a Machine that is able to reason using Knowledge.


Tags: theory, consequence, formulas
Categories: Concept
Parent: Logic

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