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First Order Logic

Logic is the foundation of knowledge representation.

Particularly in the form of predicate logic which is also known as First Order Logic. Logic offers formal languages. For expressing knowledge and provides a well-understood formal semantics. In most logics, the meanings of sentences are defined without the need to make it operational. An important element of logic is the ability to have automated reasoners. That can infer conclusions from the given knowledge:

“Note that knowledge representation and intelligent reasoning are always intertwined, both in the human mind and in AI” – Gasevic, 2009 pp.5

Inference enables the discovery of new facts from existing fact. The following is an example of inference. Suppose that all doctors are department members. That all department members are staff members. That Chris is a doctor (Dr). In predicate logic the information is expressed as follows:

Dr(X) → Department(X)
Department(X) → staff(X)
Then it can be inferred that:
Department (Chris)
Dr(X) → staff(X)

So from the first three statements.

It is concluded that Chris is a member of staff within a department of doctors. This form of reasoning and inference is an area that AI has focused on for many years. Similar concepts are needed for the success of the Semantic Web. However there is an issue with inference. It introduces scalability issues. Because of the complexity of performing reasoning over huge amounts of distributed facts. Logic is important in the field of Semantics. It provides a high-level language. In which knowledge can be expressed in a transparent way.

A first order logic language consists of logical and non-logical symbols.

The logical symbols represent quantification, implication, conjunction and disjunction. The non-logical symbols are constants, predicates, functions, and variables. Constants are symbols that begin with a lowercase letter. Variables are symbols that begin with an uppercase letter. Propositions are represented using arguments. Objects of propositions and predicates are assertions about objects. Knowledge represented with first-order logic is written in the form of predicates and rules. A predicate can be defined as:

“An operator in logic which returns either true or false.”

Reasoning with first-order logic is performed using predicates, rules, and general rules of inference to derive conclusions. The concepts that have been developed using first order logic have spawned various other logic languages. The main area regarding the Semantic Web is the use of description logics.