- Characteristics of logic programming
- Truth and logical deduction
- First order logic
- Clausal form
- Artificial intelligence
- Logic programming examples
- Example 1
- Example 2
- Query
- Other inquiries
- References
The logic programming is a programming paradigm that uses the logic circuits rather than just mathematical functions to control how the facts and rules are set.
Instead of a carefully structured flow of control that dictates when to execute and how to evaluate function calls or other instructions, the logical rules of the program are written as clauses or logical predicates.
Examples of logic programming in Prolog. Source: By Kuldeepsheoran1 - screenshot, CC BY-SA 3.0, wikimedia commons
This approach, which is often used in genetic and evolutionary programming, generally tells a model what goal to achieve, rather than how to achieve it.
Each rule contains a header and a body with a formalized logic, rather than an executable mathematical function. For example, "And is true (header): if C1, C2, and C3 are true (body)." The facts or results are expressed without a body, such as "And it is true."
However, with some programming languages like Prolog, imperative programming can also be included to tell the model how to solve certain problems. For example, "To solve Y, add C1, C2, and C3."
Characteristics of logic programming
Logic programming is substantially different from the other existing programming strategies. Instead of giving instructions to a computer with the program, relationships between objects are established. In this way the computer can reason these relationships and thus reach logical solutions.
Within a logic program there are two main sets of code: facts and rules. The rules are applied to the facts in order to gain knowledge about the environment.
Truth and logical deduction
Logic programs can be deciphered through two important concepts: truth and logical deduction. The truth comes out whether the calculation in the program is true or not, under the implementation of the program symbols. Logical deduction determines whether a logical clause is a consequence of the program.
These instructions will always be interpreted as logical sentences and clauses, the result of their execution being a logical consequence of the calculations it contains.
First order logic
It is an offshoot of propositional logic. Consider whether objects are true or false from a partial world perspective, called a domain. Logic programming is based on a generalization of first-order logic.
This logic is made up of syntax and semantics. Syntax is the formal language used to express concepts. On the other hand, the semantics of first-order logical formulas indicate how to determine the true value of any formula.
This logic is based on an alphabet and a first-order language, as well as a set of axioms and inference rules.
Clausal form
It is a subset of first-order logic. It has a normalized form where a statement is defined by a universal prefix or chain of universal quantifiers, and a free set of quantifiers in the clause.
When requesting a query to the program, the body of the clause whose header may coincide will be considered. This is the same as applying an inference rule in logic.
As a step in the inference, two clauses are chosen that have as property that one contains a disjunctive X (a positive literal) and the other contains a disjunctive ¬X (a negative literal). These tradeoffs are known as complementary.
From these two initial clauses a new resolutive clause is built using all the literals, except the complementary ones.
Artificial intelligence
Logic programming is a methodology that is used to make computers deduce, because it is useful to represent knowledge. Logic is used to represent knowledge and inference to handle it.
The logic used to represent knowledge is the clausal form. It is used because first-order logic is well understood and capable of representing all computational problems.
Prolog is a programming language that is based on the ideas of logic programming. The idea of Prolog is to make logic look like a programming language.
Logic programming examples
Example 1
- Fact: Rubí is a cat.
- Rule: all cats have teeth.
- Consultation: Does Rubí have teeth?
- Conclusion: yes.
The rule "all cats have teeth" can be applied to Ruby, because there is a fact that says "Ruby is a cat." This example is not written with any syntax for a real programming language.
Example 2
This example can be seen written in Prolog, as it is one of the most popular logic programming languages:
- feminine (alissa).
- masculine (bobby).
- masculine (carlos).
- feminine (doris).
- son_of (doris, carlos).
- son_of (carlos, bobby).
- son_of (doris, alissa).
- father_of (F, P): - male (F), son_of (P, F).
This program becomes difficult to read, because Prolog is notably different from other languages. Any code component that resembles "feminine (alissa)." it is a fact.
One rule is "father_of (F, P): - male (F), child_of (P, F)". The symbol ": -" can be read as "is true if". Capital letters mean that variables can be applied to any object, so F could stand for carlos, doris, alissa, or bobby. This code can be translated as:
- Alissa is a woman.
- Bobby is a man.
- Carlos is a man.
- Doris is a woman.
- Doris is Carlos's daughter.
- Carlos is Bobby's son.
- Doris is Alissa's daughter.
- «F is the father of P» is true if F is a man and if P is the son of F.
Query
Suppose you want to consult the program for more information. You can search asking to find whose father Bobby is with:? - father_of (bobby, X). The system will indicate the following answer: X = Carlos.
In this case, a relationship is being passed where one of its values is a variable. What Prolog did was apply different objects to this relationship until one of them was logically solid.
Carlos's only father is Bobby, and Bobby is male. This satisfied the rule "father_of (F, P): - masculine (F), son_of (P, F)." When X equals "carlos," the logic is sound.
Other inquiries
Other more general queries can be made to Prolog, which cause the system to generate multiple results:
-? - parent_of (Parent, Child).
- Father = bobby
- Child = Carlos
- Father = Carlos
- Child = doris
As has been observed, logic programming does not require having the information that alissa or bobby are people in order to obtain knowledge about them. In fact, it is not necessary to indicate that there is a concept called person.
In most non-logical programming languages, you would have to define these concepts first before you can write programs that process information about people.
References
- Deep AI (2020). Logic Programming. Taken from: deepai.org.
- Wikiversity (2020). Theory of Programming Languages / Logic Programming. Taken from: en.wikiversity.org.
- Imperial College London (2006). Logic Programming. Taken from: doc.ic.ac.uk.
- Jia-Huai You (2020). Introduction to Logic Programming. University of Alberta. Taken from: eng.ucy.ac.cy.
- C2 Wiki (2020). Logic Programming. Taken from: wiki.c2.com.