Question

How is Logics such as (Predicate Logic, Propositional Logic, and Logical Reasoning) used in Computer Science?

Examples of how it implies to computer science would be great.

Answer 1

Predicate logic, Propositional logic and Logical Reasoning in Computer Science

Propositional logic

• It is also a part of Artificial Intelligence study
• It is about asserting a statement whether it is true or false based on proved facts and validating it as Boolean result
• Propositional logic can be used for encoding arguments. The arguments are involved in natural languages.
• It can help validating using truth tables
• Examples are
  • “Mango is yellow”
  • “Earth is spherical” ,
  • 2+2 =4
• In computer science it finds it way as
  • digital electronic circuits
  • Conditions using loops like for, while , do while switch case , if , else, in programming
  • Boolean operators in programming
  • Database queries

Technical Example

1. A :Good televisions are not cheap
2. B : Cheap televisions are not good
3. C : A implies B
4. D : B implies A<>
5. E: A is equivalent to B

Result : C, D and E are correct using a truth table as below explained

a and b are 2 propositions

a : Good televisions
b: cheap televisions

A and B can be expressed as follows

A: a --> ~b
B: b--> ~a

Let u check using Truth table as below

a b ~a ~ b A B
T T F F F F
T F F T T T
F T T F T T
F F T T T T

Since A and B are equal, C, D, E are correct.

Predicate Logic

Predicate logic also part of Artificial Intelligence and it is the general notation of a property or a characteristic of a subject referred in a statement

Example:

Create definition and Premises to prove using Predicate Logic.

L :≡ Labrador ( is a popular breed of a dog)

A (x) :≡ " x is an animal"

M(x) :≡ "x is Mortal"

A(L) - Labrador is a animal

x A(x) -> M(X) - "All animals are mortal"

Result : It is proved that Labrador is mortal

Logical Resulting

• Logical Reasoning is the key aspect in computer science and software programming
• Logical reasoning is applied in problem solving
• Logical reasoning is applied in Machine Learning algorithms to predict a output as true or false based on input variables
• Based on input data , one system can conclude a result
• Computer science uses set of rules , applied by algorithms using logical reasoning
•   Logical reasoning is reaching into conclusions based on Propositional logic , predicate logic too.

Examples which I explained in above are applicable to logical reasoning. Let me some more below

• When a fruit is round , big ,depressed on top and red in colour it can be an apple . Saying apple based on the given data , is the conclusion as a logical reasoning. This kind of conclusion and analysis can be done using Machine Learning algorithms by training the machine with data about fruits which will group and classify based on their unique features and with the predefined output as apple, orange or banana etc as part of Supervised Learning .
• In an Unsupervised Learning, the input variables will be trained to the machine without output variable as the machine . So the machine will group the fruits based on its features like colour (red, yellow, green) and produce an output variable without seeing it earlier and without predefined output .