First Order Logic

Created on March 1, 2013, 7:45 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:34 p.m.

First Order Logic (FOL) is very powerful. In First Order Logic one has Quantifiers. Quantifiers, or Quantors, allow Assertion of Sets of Objects even without naming these Objects explicitly.

So one can make Statements like All Humans are mortal and than one can pick out one Human and say it is a Human and because one previously stated that all Humans are mortal it can be deduced that Hevok must be moral too. Thus, one can make Deductions out of these Sentences/Statements. Normally one has a general Statement, then a special Statements and then one can infer implicit knowledge that is given in the Generalization. FOL is perfectly suited for a Description of Ontologies, but it is rather expressive, which means it is much more too expressive. On the other hand it is also very complex when it comes to Computation. It is not only complex some of the Calculations in Logical Calculus for First Order Logic are not decidable, i.e. not computable.

Overall the expressiveness of the First order Logic means for Models it is rather Bulky. It is also very Bulky because one can express the same the Subject, the Knowledge in various different Forms and therefore one has the problem to find a unique Form or unique Representation for the Knowledge. Thus, it is difficult to achieve Consensus about a Model. Another issue is that it is rather complex to Proof if one wants to proof the Correctness or Completeness of Assertions.

One needs to look at some better suited Fragments of First Order Logic. Something that lies between Propositional Logic and First Order Logic. It need to be something that is almost as expressive as First Order Logic but does not have its Disadvantages like for example the complexity or the expressiveness as well as the ambiguity.

  • In the First Order Logic (FOL) Quantors allow Assertions about Sets of Objects, without naming the Objects explicitly.

    All Humans are mortal. Hevok is a Human. Hevok is mortal.

  • FOL is perfectly suited for the Description of Ontologies, but ..

    • FOL is rather expressive,
    • therefore also rather bulky for Modeling,
    • difficult to achieve consensus in Modeling and
    • rather complex to Proof (Correctness and Completeness of Assertions)
  • Therefore: look for some well suited Fragment of FOL!

FOL as Semantic Web Language?

First order Logic is quite fine it can do everything but its very complicated, very expressive, its bulky and its complex. One can compare this to Programming Languages. Of course one can do everything with a higher Programming Language, like Object-orientated Programming Languages, also with Assemblers (Assembly Languages) but one does it not because it is much too complicated and much too trouble. It is the same for First Order Logic, as it is very expressive but its too bulky for Modeling and the Problem is that it is difficult to find Consensus in Modeling. Another point is that from a Proof-theoretical view it is very complex as it is only semi-decidable and not fully decidable. On the other hand if one wants to put it on the Web, First Order Logic is also not a Markup Language.

  • Why not simply take FOL for Ontologies?
  • FOL can do everything...
  • FOL has
    • high expressivity
    • too bulky for Modeling
    • not appropriate to find Consensus in Modeling
    • proof theoretically very complex (semi-decidable)
  • FOL is also not a Markup Language

Look for an appropriate Fragment of FOL


Tags: quantification, reasoning, statements
Parent: Logic

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