Robotic Rational Reasoning!

Robotic Rational Reasoning! P.H.S. Torr

Book • An Introduction to Probability and Inductive Logic • Ian Hacking • In library

Resources • http://plato.stanford.edu/entries/probability-interpret/

Machine Learning • Suppose we are to design a robot • How is to learn about the world? • What is learning? • How can it make decisions on what actions to take?

Types of Question we want an AI construct to answer… • Should the robot turn left or right down a road • Do we perform an operation or not? • Is this person a terrorist or not? • Does it think the world is flat or round? (are scientific laws amenable to inference)?

Example (from Jaynes) Suppose some dark night a policeman walks down a street, apparently deserted; but suddenly he hears a burglar alarm, looks across the street, and sees a jewellery store with a broken window. Then a gentleman wearing a mask comes crawling out through the broken window, carrying a bag which turns out to be full of expensive jewellery. The policeman doesn't hesitate at all in deciding that this gentleman is dishonest. But by what reasoning process does he arrive at this conclusion?

Computer Vision • What inference should the robot draw from this image? • How shall we operationalize this inference (e.g. make a computer program to carry out inference)?

Discuss • How should the robot decide the following: • Whether the person shown previously is a burglar?

Discuss • How should the robot decide upon the following actions: • Whether to phone the police or not?

More Generally • We would like the robot to be able to rationally decide • Whether smoking causes cancer • Whether to believe in God • We would like the robot to be able to also decide how to rationally act • In any situation given the evidence. • E.g. robotically guided vehicle (autopilot).

What is Inference? Dictionary • in·fer·ence (ĭn'fər-əns) n. • The act or process of deriving logical conclusions from premises known or assumed to be true. • The act of reasoning from factual knowledge or evidence. • Something inferred. • Usage.To draw inferences has been said to be the great business of life.

Inference To draw inferences has been said to be the great business of life. Every one has daily, hourly, and momentary need of ascertaining facts which he has not directly observed; not from any general purpose of adding to his stock of knowledge, but because the facts themselves are of importance to his interests or to his occupations. Introduction from the Longman's 1884 edition of the System of Logic. John Stuart Mill (1843)

Epistemology • "is derived from the Greek words episteme, which means knowledge, and logos, which means theory. It is the branch of philosophy that addresses the philosophical problems surrounding the theory of knowledge. It answers many questions concerning what knowledge is, how it is obtained, and what makes it knowledge. " • Excerpt from - "Rhetoric & Epistemology" by Nathan T. Floyd of the Georgia Institute of Technology.

Logic • logic, the systematic study of valid inference. • Logic can take many forms.

Types of Logical Argument • Deductive; Reasoning from the general to the specific. • Inductive; The process of deriving general principles from particular facts or instances. • Abductive; reasoning based on the principle of inference to the best explanation. (Charles Pierce). • Doxastic; to do with belief.

Deductive Argument • A deductive argument offers two or more assertions that lead automatically to a conclusion. • Though they are not always phrased in syllogistic form, deductive arguments can usually be phrased as "syllogisms," or as brief, mathematical statements in which the premises lead inexorably to the conclusion.

Syllogisms • Syllogism; A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion; for example, • All humans are mortal, the major premise, • I am a human, the minor premise, therefore, • I am mortal, the conclusion. • Reasoning from the general to the specific; deduction.

Deductive Argument • As long as the first two sentences in this argument are true, there can be no doubt that the final statement is correct--it is a matter of mathematical certainty. • Deductive arguments are not spoken of as "true" or "false," but as "sound" or "unsound.“ • A sound argument is one in which the premises guarantee the conclusions, and an unsound argument is one in which the premises do not guarantee the conclusions. • A deduction can be completely true, yet unsound. It can also be sound, yet demonstrably untrue

Deduction • The major premise is a statement of general truth dealing with categories (sets) rather than individual examples: • All humans are mortal • The subject section of the major premise (All humans) is known as the antecedent; the predicate section of the major premise (are mortal) is known as the consequent.

Deduction • The minor premise is a statement of particular truth dealing with a specific instance governed by the major premise (an element of the set): • “I am human” • The conclusion is the statement derived from the minor premises relationship to the major premise: I am mortal.

Deductive logic • In Western thought, systematic logic is considered to have begun with Aristotle's collection of treatises, the Organon [tool]. • Aristotle introduced the use of variables: While his contemporaries illustrated principles by the use of examples, Aristotle generalized, as in: All x are y; all y are z; therefore, all x are z. • Aristotle posited three laws as basic to all valid thought: the law of identity, A is A; the law of contradiction, A cannot be both A and not A; and the law of the excluded middle, A must be either A or not A.

Consider • Syllogism; • All people in masks are burglars • I see a man wearing a mask • The man must be a burglar Must this always be true?

Inductive Reasoning

Inductive Reasoning • If you were to measure 20 carrots, and found that they were all between six and eight inches long, you might conclude that all carrots were in that size range. The manner of logic you used to draw your conclusion is called inductive reasoning.

Inductive Reasoning • According to the philosopher John Stuart Mill, its chief proponent, we are using inductive reasoning when we conclude • "that what is true of certain individuals of a class, is true of the whole class, • or what is true at a certain time will be true in similar circumstances at all times."

Example • Observations; • Observation: The man is wearing a mask • Observation: He is climbing in via the window • Prior Experience: People normally do not wear masks or climb in via windows unless they are up to no good. • Conclusion: The man is probably a burglar.

Question • How might we design an algorithm for the robot to perform inductive reasoning ? • Are there any rules we can use to help us (perhaps we can deduce the rules of inductive reasoning deductively? i.e. by the laws of mathematics).

Burglary Although we can not be certain it seems probable that this man is a burglar. The word probability derives from the Latin probare (to prove, or to test).

Prior Knowledge in Vision • We resolve complex scenes on the basis of prior knowledge, what we have previously learned about the world.

Illusions • This is even true for low level vision (we can’t help ourselves). • We are so tuned to natural scenes, that our prior information dominates the evidences of our eyes.

Illusion

Questions: • More on probability later • However first a quick test…

Deductively valid? Premise: All cars have wheels Premise: All wheels are round Conclusion: All cars have round wheels -- Premise: I have a diamond Premise: Most diamonds are shiny Premise: My diamond is shiny --- Premise: John is 93 Conclusion: John will not do a double back flip today

Inductive vs. Deductive Reasoning • Deductive reasoning: • conclusion follows logically from premises: CERTAIN • Inductive reasoning: • conclusion is likely based on premises (evidence). • Does not use syllogisms • involves a degree of uncertainty • Most reasoning in real-world is based on induction • How do people reason with uncertainty? • What is the right way to reason with uncertainty?

Problem • Not everyone accepts induction is valid:

Problem: Karl Popper • Popper claims that there is no such thing as induction and that deduction is all that we need in science. • Was he right?

Popperism • In place of induction, Popper offers the method of conjecture and refutation. • Scientific hypotheses are offered as bold conjectures (guesses) about the nature of the world. • In testing these conjectures through empirical experiment, we cannot give positive inductive reasons for thinking that they are true. • But we can give reasons for thinking they are false

Popper’s Scientific Process • If H then O Then not O Therefore, not H • This pattern of reasoning is deductively valid (to see this try to suppose that the premises are true and the conclusion is false. If the conclusion were false, then 'H' would be true. And, given this and the truth of the first premise, 'O' would follow. But 'O' contradicts ‘not O” which is asserted by the second premise. So it is not possible for the premises to be true and the conclusion false. In other words, the pattern of reasoning here is deductively valid.)

Falsifiability • Popper's method of conjecture and refutation suggests another criterion for distinguishing science from non-science. • That is, that we can take a hypothesis, a proposed explanation, to be investigated scientifically if and only if it is falsifiable. • For a hypothesis to be falsifiable does not mean that that it will be proven false or that it can be shown to be false • Rather, to say that a claim is falsifiable is just to say that we can state some possible observable conditions under which we would judge the claim to be false.

Popper’s accident • Suppose a car comes speeding towards you, you have never been hit by a car… • You have two hypotheses • The car will hurt you if it hits you • The car will bounce off you • Which hypothesis do you think more probable? • How would you act on the basis of each hypothesis? • Would you want to falsify one of the theories?

Teapots • There are many theories that are equally not falsified by observations • Bertrand Russell’s tea pot. • There is error in measurement, can anything really be falsified with certainty?

Hume on Induction • The classic philosophical treatment justification for inductive reasoning, was by the Scotsman David Hume.

Hume on Induction • Hume highlighted the fact that our everyday reasoning depends on patterns of repeated experience rather than deductively valid arguments. • For example we believe that bread will nourish us because it has in the past, but it is at least conceivable that bread in the future will poison us.

Hume on Induction • Someone who insisted on sound deductive justifications for everything would starve to death, said Hume. • Instead of unproductive radical skepticism about everything, he advocated a practical skepticism based on common-sense, where the inevitability of induction is accepted.

Hume • In other words, although we can not prove induction (by logic) • We might want our robot to behave as induction were valid. • i.e. he should use his past experience.

Bertrand Russell . What these arguments prove--and I do not think the proof can be controverted--is, that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle science is impossible.

The Irrationalists? • Science as we know it has been built on induction. • Stove refers to those who deny induction (Hume and Popper) as the irrationalists. • Popper and After: Four Modern Irrationalists, Pergamon Press, 1982. David Charles Stove. • http://www.geocities.com/ResearchTriangle/Facility/4118/dcs/popper/popper.html

Plan • Having introduced the puzzle of induction the course of this lecture will continue to show one of the most intriguing attempts to solve it. • Most of the development of which have only occurred in the past 100 years.

Probability As mentioned before it seems to us to make sense to say This man is probably a burglar. What does probability mean?

What has a valid Probability Consider the Statements: • The next roll of the dice will be a six. • Blair will win the next election. • The end of the universe is one billion years distant. • The 1000th number of pi is 9. • A coin is in my left or right hand.

Robotic Rational Reasoning!