View source for Artificial Intelligence/Logic/Representation/Propositional calculus

==Zero-order logic or the Propositional calculus==
The '''zero-order logic''', often referred to as the '''propotional calculus''' are defined in the context of [[w:Boolean algebra|Boolean constants]], where two or more values are computed against each other to produce an accurate description of a''concept''. Each variable used in the calculus holds a value for it, which is either true to the context or false<sup>1</sup>. 

'''Propositional logic''' deals with the determination of the ''truth'' of a sentence. An allowable sentence is called the '''syntax''' of proposition. A syntax or sentence holds various '''propositional symbols''', where each symbol holds a proposition that can either be <code>true</code> or <code>false</code>. The names of the symbols can be anything from alphabets like <code>a</code>, <code>b</code> or <code>c</code> to symbols like <math>\alpha</math>, <math>\beta</math> or <math>\gamma</math> to variable names like <code>IsOld</code>, and may hold meaning relative to their contexts in the concept. Although, two propositions are constant as per the syntax and have a fixed meaning. They are:
* <code>True</code> - proposition that is ''always-true''.
* <code>False</code> - proposition that is ''always-false''<sup>2</sup>.

In mathematical terms, these values would pronounce more like this:


<center><math>u \Leftarrow a \wedge b \wedge c</math></center>


In simple terms this means that an object is an instance of a concept <code>u</code> if the conditions <code>a</code>, <code>b</code> and <code>c</code> hold true simultaneously. So, for instance, we are given with a concept that says, ''one is eligible to drive a car if one has a license, a car and a knowledge of driving''. To state this in propositional calculus, you'd have to state this in the following mathematical notation:


<center><math>CanDriveCar \Leftarrow HasLicense \wedge HasCar \wedge KnowsHowToDrive </math></center>


However simple to denote, the zero-order logic is only capable of describing concepts in a limited context and do not hold much of a ''descriptive power''.

==Notes==
# Kubat, Bratko, Ivan and Michalski, Ryszard. ''Machine Learning and Data Mining: Methods and Applications/A Review of Machine Learning Methods''. 1998. ISBN 0471971995. John Wiley: New York.
# Russell, Stuart and Norvig, Peter. ''Artificial Intelligence: A modern approach''. 2003. ISBN 0130803022. Prentice Hall:New Jersey.