Abstract of First Order Logic

            First order logic language defines the syntax, provide examples and elaborate the semantics. As language of knowledge representation First order logic and predicate logic are relatively better than the propositional logic. Propositional logic has some laminations. While first order logic (FOL) and predicate logic covers not only the propositional logic but also cover additional areas.  In this paper, the history of first order logic is discussed as GOFAI that represents the Good Old- Fashion Artificial Intelligence. Frege introduced the first satisfied FOL to implement in the field of mathematics. First order Logic covers the functions, objects, and relations. The basic elements of First Order Logic (FOL) are sentences and predicate. The paper also presents several examples related to the symbols used in the first order logic sentences.

Key words of First Order Logic

The key words related to the topic and information presented in this paper are presented below:

First Order Logic (FOL), Predicate logic, Propositional logic, History of predicate logic, Evolution in the First order logic (FOL) and predicate logic, Artificial intelligence, First Order Logic (FOL) in Artificial intelligence, predicate logic symbols, Knowledge based agents, knowledge based language. 

Introduction of First Order Logic

              Knowledge based languages provide information and knowledge about certain facts and realities on the basis of logic. The concept of First order logic is one of these knowledge based languages.  In the beginning propositional logic was quite common in the programming and Knowledge based language [1]. However, the limitations of the propositional logic was a reason that contributed the most in introducing the new logic oriented languages in the market. In the past years great scientists and philosophers worked on the first order logic and other logic related languages that present knowledge.

               Artificial intelligence works to perform several installed functions by utilizing artificial intelligence [2]. Computer, calculators, and robots work on the principles of artificial intelligence. The installed artificial intelligent behavior encourage the system to understand the requirements and present the appropriate answer on the basis of analysis [3]. The scientist presented the artificial intelligence to help the human being lend a happy and relaxed life with minimum miseries and complexity. In this way, First order logic and predicate logic support the artificial intelligence and provide knowledge and fact oriented information to the systems. [3]  In this paper, the theory of first order logic is presented as a knowledge representation language. The paper also covers the history of the predicate logic and application of the First order logic (FOL) in the artificial intelligence.        

Critical Literature Review of First Order Logic

            To study the First Order Logic (FOL) as the knowledge representation language and predicate logic several research studies and books are reviewed as literature. Literature review contains information collected from the secondary and primary sources of data. 

            In accordance with the studies, symbolized reasoning that refers to the broken predicates and subjects are known as first order logic (FOL). The language of the first order (also predicates) is a famous theory related to the knowledge representation which is the extension of the language of classical logic [1]. First order logic has also significant value as a tool of reasoning and knowledge representation. In FOL broken predicate and subject are resulted from statements and sentences. However, the subject should be only a single one in the FOL. FOL is also entitled as first order functional calculus (FOFC) and first order predicate calculus (FOPC) [1]. Basically, First order logic (FOL) is based on the collections and group of formal systems that are commonly in use in the fields of philosophy, mathematics and linguistics. In the theories of first order logic (FOL) there is presented strong association in sets and predicates. Predicate logic is the complex term that covers several dimensions. 

           In accordance to the studies by Gabbay, Thagard, Woods, and Jacquette (in 2006), predicate logic symbolizes and presents the systematic procedures sets that support the idea that some formulae can be or cannot be driven logically from other available formulae [1]. Considering such qualities of predicate logic programmers are using it in the artificial intelligence to enable the systems to solve problems in the appropriate manner and on the basis of logic. For instance in the predicate logic the sentence “some birds can fly” refers to the logical sentence that “all birds cannot fly” [2].

          According to the literature, Knowledge based agents are directly supported by inference systems and knowledge base [2]. Basically knowledge base covers the set based on the real knowledge and facts related to the universe. In this system, the representations are known as sentences. Knowledge based agents enable the logic based sentences to represent and express the reality and facts concerning with a particular situation [1]. FOL is also considered an extension or advanced concept of propositional logic as both works for the logic and facts.  

         According to the research, First order logic has several syntax elements that are predicates, variables, equality, functions, constants, quantifiers, and connectives. Opposite to the propositional logic, First order logic (FOL) also contains objects, functions, and relations. Examples of objects are wars, people, theories, centuries, and games. While examples of relations include multistoried, owns part of, inside, red, round and bogus. Functions in first order logic include one more than, father of, and end of.

         According to the Goldrei, (2005), the propositional logic components, constants and propositional variables all include in the predicate logic. Basically propositional logic was unable to cover all types of assertions being in use of mathematics and computer sciences [3]. While predicate logic also covers issue what is not covered by the propositional logic. Moreover, the terms known as quantifiers and predicates are also covered by the predicate logic [3]. Predicate and quantifiers are in fact replacement of the pronoun and nouns in the programming. In other words, predicates are expressions of the single or more than 1 variables that concern with the specific type of domains [2].

            History of Predicate Logic is as old as the concept of logic [4]. In the early 1800s, predicate logic was the main concerning the topic of the German philosophers [2]. The first system based on the predicate logic was presented by the Gottlob Frege. Therefore, it is considered that the origin of predicate logic is German philosophy. The first predicate logic system was capable to cover the negation, conjunction, biconitionals, disjunctions, and quantifiers. The generality of the predicate logic was the departure from the thoughts of Aristotle [4]. The concepts of first order logic and predicate logic are changed a lot with the time.

            Literature studies indicate that with the passage of time improvements are made in the predicate logic. In some areas, false concepts are eradicated and new concepts introduced to make the predicate logic more efficient to cover facts representations and logic [5]. According to the history of predicate logic, Frege was researching on the predicate logic to find out the secrets of mathematics. Bertrand Russell also worked on the predicate logic with the relatively same ambition of finding the solution to paradox [1]. Other than Russell, there were also other great philosophers as Kurt Godel and Alfred Traski who conducted research on the predicate logic to ensure improvement. Formal interpretation and advanced predicate logic are the results of efforts done by Alfred Tarski in 1930 [3].   

             In the predicate, logic and first order logic (FOL) symbols are used to represents the logic and facts. In predicate logic, the capital letter is symbolized to the predicate and lower case letters to subjects. Basically, symbols are in use to stand for certain kind of predicate in the sentences. The symbols used in predicate logic can represent the multiple variables [5]. A web-article published by Philosophy-index.com presented an example related to the symbols of predicates logic. According to the article, if we want to write a sentence “Wanda likes George” in symbolized form of predicate logic we will write as L⁽²⁾ Lgw [4].    

             In the literature written on the artificial intelligence (AI) and programming systems, the knowledge based agent _ First order logic (FOL) is considered as GOFAI abbreviated form of Good Old- Fashioned Artificial Intelligence [2]. In the beginning, FOL faced critique from the research studies conducted on artificial intelligence. Nevertheless, now it is considered as Good old fashioned artificial intelligence because of the efforts and contribution did by the first order logic in the progress of artificial intelligence [6]. In accordance with the Smullyan, artificial intelligence refers to the study of intelligent behaviors that can be achieved through the means of computations. In artificial intelligence central idea is to develop intelligent behavior with the purpose to generate the ability of problem solving [1].  First order logic provides logic and facts that work as the basis behind the functionality of artificial intelligent behavior.

            Summarizing all the information presented in the literature review of the paper, we can say that first order logic provides logic oriented information and benefit the artificial intelligence system in several ways but there are some limitations that are causing to decrease the value of the first order logic. FOL cannot be considered as best approach in artificial intelligence as it is an old approach or knowledge based language.