On Logic and more logic... through predicates...

PREDICATE LOGIC

When we were in school, as early as primary or middle school for others, we were taught that a sentence is a [special kind of] proposition. Later on, during our high-school years, more formally, we learnt that a sentence is defined as:

A [special kind of] proposition that has both syntactical and semantical completeness.

Furthermore, it was explained to us that a sentence has two main parts, namely:

·     A subject

·     A predicate

Both the subject and the predicate are divided into subcomponents and become the study of many linguistic researchers, who are still fascinated by the intricasies of every specific language.

For instance, the subject can be composed of an article, a noun and an adjective.

Likewise, the predicate can be composed, for instance, of a verb, and direct object (AKA, as [complement] direct object, e.g., a noun), an indirect object and an adverb.

In Artificial Intelligence, there is Predicate Logic. A predicate is a verb phrase template that describes a property of objects, or a relationship among objects represented by the variables.

Besides, the propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence.

While propositional logic deals with simple declarative propositions, first-order logic additionally covers predicates and quantification. 

A predicate takes an entity or entities in the domain of discourse as input and outputs either True or False.

·     For instance, the assertion "y is greater than 21", where y is a variable, is not a proposition because you can not tell whether it is true or false unless you know the value of y.

·     Thus the propositional logic cannot be dealt with in such sentences.

·     However, such assertions appear quite often in mathematics and we want to attain an inference based upon those assertions.

Predicate Logic has a special value in ontology and classification as well as in taxonomy and semantic network logic.   

This lecture focuses on demystifying the key concepts of predicate logic and implicitly their applications in AI.

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