What is logical reasoning?

If we consider that, there exist about 20 - 30 different logics, for instance, Temporal Logic, Epistemic Logic, Propositional logic, Modal Logic, Default logic and so on, then Logical reasoning can be defined with these three steps:

1. Formalize the natural language sentence with logical symbols, such as (P, Q, box, diamond, ...)
2. Write the process of reasoning with the symbols
3. Use axioms, postulates and theorems of that specific logical language (or a combination of them) to conclude a certain fact that does not exist in the preliminary statements.

Claim 1 - Human can NOT do logical reasoning beyond a certain simple level

For instance you can go to the site of Angela Robot and check some of those temporal logic theorems that she is presenting. Try to prove them without paper, pencil and hours of prior learning the methods. I claim that you can not do it. No human can do it. But a computer can. Our brain is not designed to do it. We do not have the facilities required to be able to do it. But a computer can. This is not your fault. In return, you can be happy that a computer can not swim (yet).

Claim 2 - A not-trained human, does reason, but incorrect (most of the time)

The only way to prove that a conclusion is correct or not, is to follow above three steps and check that formulas are correct or not. Example of an incorrect reasoning is presented in the penguin joke. If you are interested, then use the following formulas and prove "why the penguin is incorrect" and send us your proof and get a complimentary user name and password to access our (friend account) membership for the Robots.

What type of Logic our Robots use?

Our Robots are equipped with common-sense reasoning and first order predicate logic.

What is common-sense reasoning?

Common-sense reasoning requires a huge amount of data in the dBase. We humans do have it. We have learned many facts. That is why (so far) we can reason better than a computer. (if the dBase of the computer is small) Please look at the examples:

Example one

• Jo saw a bird flying over the city
• Jo saw the tree flying over the city

We know that Jo saw the tree --- comma, while HE was flying --- (by airplane) over the city. Because we know that:

• Tree does not fly
• Jo can not fly
• Jo can fly, if he is in an airplane

These three sentences are not in the example but they are in the dBase of our brain. Therefore we do not conclude that:
Jo saw, that, a tree was flying.

If you feed a computer with thousands (preferably millions) of common-sense knowledge sentences, (like an adult human) and give the ability of using the formulas for reasoning to the robot, then computer can do common-sense reasoning, better than a human. Example two and three are not described but you can work it out.

Example two

• Soldiers arrested the people because THEY were afraid of violence.
• Soldiers arrested the people because THEY were promoting violence.
• They = Soldiers - People
  

Example three

• Jo saw a cat in the store window and decided to adopt IT.
• Jo saw a cat in the store window and moved his face toward IT.
• It = Cat - Window
  

Example four

This is an example for a robot that is driving a car. Comparing with a human who is driving a car. Preceptors of the robot (or eye of the human) show that a person is crossing the road. Question is this; Do I slow down or not?

• Situation 1 - Pedestrian is young.
  
• Situation 2 - Pedestrian is old.
  

If a human is driving, because he knows these statements in his common-sense dBase (in his brain), that

• Old people usually are walking slower than young people
  
• An old person might become stressed and might stop in the middle of the road if he sees that a fast car is coming toward him, but a young person might just run
  

Then a human driver, if sees an old person, slows down and if he sees a young person, most probably does not slow down. His reasoning is correct because he has those millions of facts in his brain.

If you do not give all of that information, that seems very simple, but necessary for our day to day reasoning, and ask the robot to drive. I guess, most probably, it could be considered a dangerous driver. It is not fault of the robot, it is fault of the programmer that gave the Robot a small dBase. Reasoning engine of the robot might work correctly, but because its EXPERIENCE (number of common-sense facts) is not enough, it might make mistakes.

Therefore, a good common-sense reasoning engine requires a huge dBase of facts.

How big is the dBase of facts of our robots?

There are two versions.

• Demonstration version
• Commercial version

The demonstration version has a very small dBase, just to demonstrate how it works. The commercial version has all of those thousands of facts that are written in the (specifications) page of our site.

Formulas that our Robots know for Logical Reasoning

Modus Tollens	(P=>Q, ~Q) => ~P
Modus Ponens	(P=>Q, P) => Q
Hypothetical Syllogism	(P=>Q, Q=>R )=>(P=>R)
Simplification	(P & Q) => P
Conjunction	(P, Q) => (P&Q)
Disjunctive Syllogism	[(P v Q), ~P ] => Q
Addition	P => ( P v Q)
Reductio Ad Absurdum	[P, (Q &~ Q)] => ~P
Constructive Dilemma	[(P => Q), (R => S), (P v R)] => (Q v S)
	And a combination of above

If you are a logician and are interested in knowing more about Propositional logic reasoning, Epistmeic logic reasoning and Common-Sense reasoning abilities of our Robots, then, please go to the contact page and email us. We will be happy to send you more information.