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- Logic & Programming
- Assignment
- May 23, 2018

The paper "Symbolic Logic" is a worthy example of an assignment on logic and programming.

According to Li, symbolic logic is a formalized system of deductive logic that employs symbols for various aspects of natural language (2010). The paper presents two arguments in form of modus ponens and modus tollens, after which it presents the arguments in symbols using sentence letters.

Modus Ponens

Modus ponens is a rule of inference where if one proposition implies the second proposition and the first proposition is true, then the second is also true. Example of argument:

If it is raining, I’ll not go to school. It is raining; therefore, I’ll not go to school.

It is raining (P) It is not raining (-p)

I’ll go to school (Q) I’ll not go to school (-Q) Therefore (…)

Symbol:

If P → -Q, p … -Q

Modus Tollens

It is a rule of inference where if a proposition implies the second and the second proposition is not true, then the first proposition cannot be true.

If a motion detector detects any movement, it will turn on the security alarm.

The security alarm wasn’t turned on.

Therefore, the motion detector didn’t detect any movement.

Motion detector detected movement (P) Motion detector didn’t detect any movement (-P)

The security alarm is on (Q) Security alarm is off (-Q)

Symbol

P→ Q, -Q … -P

Symbolic arguments are able to easily simplify complex English problem statements and to create a simplified model of a problem out of a complex problem for easier problem-solving.

The disadvantage is that some English arguments are too long and complex to be represented symbolically. It might lead to wrong representations by the problem solver.

According to Li, symbolic logic is a formalized system of deductive logic that employs symbols for various aspects of natural language (2010). The paper presents two arguments in form of modus ponens and modus tollens, after which it presents the arguments in symbols using sentence letters.

Modus Ponens

Modus ponens is a rule of inference where if one proposition implies the second proposition and the first proposition is true, then the second is also true. Example of argument:

If it is raining, I’ll not go to school. It is raining; therefore, I’ll not go to school.

It is raining (P) It is not raining (-p)

I’ll go to school (Q) I’ll not go to school (-Q) Therefore (…)

Symbol:

If P → -Q, p … -Q

Modus Tollens

It is a rule of inference where if a proposition implies the second and the second proposition is not true, then the first proposition cannot be true.

If a motion detector detects any movement, it will turn on the security alarm.

The security alarm wasn’t turned on.

Therefore, the motion detector didn’t detect any movement.

Motion detector detected movement (P) Motion detector didn’t detect any movement (-P)

The security alarm is on (Q) Security alarm is off (-Q)

Symbol

P→ Q, -Q … -P

Symbolic arguments are able to easily simplify complex English problem statements and to create a simplified model of a problem out of a complex problem for easier problem-solving.

The disadvantage is that some English arguments are too long and complex to be represented symbolically. It might lead to wrong representations by the problem solver.