lecture 10 - reasoning with knowledge

8/9/2019 Lecture 10 - Reasoning With Knowledge

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Knowledge Society

Lecture 10

Reasoning with Knowledge

Overview

y Many routine tasks are automatable indeed many of these are now regularly

solved by computing based devices

y Routine tasks that are not computer controlled and require people will be

outsourced to low cost countries, or low wage paying positionsy Now we need to draw facts together to make inferences and conclusions about

maintaining and sorting information and analysing information numerically

y The discipline of formalised thinking processes falls into the domain critical

thinking

What is Critical Thinking

y Many everyday distinctions are based on emotion and instinct

y Cannot be sure that the decisions we makes are reasonable ones

y The discipline of critical thinking provides us with a set of conceptual tools,

coupled with intellectual skills and strategies for making reasonable decisionsabout what to believe or do

y Critical thinking is the science of using reasoning to make up your mind, rather

than purely emotion

y Reasoning is the disciplined use of intelligence for problem solving

y Do not think of the term critical as pejorative

y Critical refers to our ability to make judgements based on facts and evidence

y The field of critical thinking is vast

y Ideally it is something that we should study and practice for the rest of our

lives

y Two important and related parts f critical thinking

o Types of reasoningo Use of logic to evaluate truth

Types of Reasoning

y Reasoning is the human capacity to use disciplined intelligence to solve

problems

y Developing arguments that take us from a premise or premises to a conclusion



y A premise is a claim offered in support of the conclusion

y Important consideration is the strength, or the degree to which we can trust,

our movement (or inference) from a premise to conclusion

y Abductive Inferencing

1. Reasoning technique that most people practice

2. Working off a hunch

3. The reasoner uses intuition to try to find connections between

seemingly unrelated facts

4. Uses the premise or remises to explain the conclusion

5. Least powerful because there may be multiple possible

explanations of the conclusion

6. Example:

Argument

y The world must be spherical in shape. The night sky

looks different in the northern and southern regions,

and this would be so if the earth were spherical.

Aristotle, Physics

Methody Abduction. HereAristotle starts with the conclusion

to try and justify it from the premise.

y Inductive Inferencing

1. If the premises of the argument are true, it is reasonable or likely,

to make the conclusion true

2. Degree or certainty is established from multiple instances of the

association of a premise or premises with a conclusion

3. Experiential in nature

4. Scientists often refer to this type of reasoning as empiricism

5. Developed in the 17th century by Sir Francis Bacon

6. Words such as probably and likely imply induction

7. Example:

E.g. 1

y Argument

o A student passed the skills test and the mid-

semester exam, always studies hard and wear

glasses, therefore, the student will pass the

subject knowledge society

y Method

o Induction. The various premises are true,

therefore the conclusion is extremely likely.

However, by no means a certainty.

y Deductive Inferencing1. Strongest for of inferencing

2. Directly derive the conclusion form a premise or a set thereof

3. If premises are true, the conclusion will be true

4. Deductive inferencing achieves absolute security in reasoning

5. Words such as certainly, necessarily and must imply a

deductive argument

6. Example:

E.g. 1



y Argument:

o All men are mortal

o Socrates is mortal

o @Socrates is mortal

y Method:

o Deduction both premises are true, thus the

conclusion is true

y This syllogism is an example of a sound argument as

both premises are true

E.g. 2

y Argument

o Every animal that has four legs is a dog

o My cat has four legs

o @My cat is a dog

y This is an unsound (invalid) argument as one of the

premises is incorrect

y First great treaties on logic written by the Greek philosopherAristotle

y Collection of rules for deductive reasoning as the basis for the study of everybranch of knowledge

y Use of language is important when trying to determine the inferencing method

being used (and hence the strength of the argument)

y The form in which we write an argument is very important

1. All men are mortal

2. Socrates is a man

3. @ Socrates is mortal

It is impossible to deny the plausibility of the argument

seeing it in this form

This is a valid form of deductive argument

y However, consider the slightly modified argument 1. All emus are birds

2. All cockatoos are birds

3. @All emus are cockatoos

Appears reasonable but the conclusion is not necessarily

true

1. All Queenslanders are Australians

2. All Victorians are Australians

3. @All Victorians are Queenslanders

This is FORMAL FALLACY

Universal and Existential

y So far we have used universal statements

y Distinguished by the use of the word All

y The other form of statement is called the existential

y Usually beginning with SOME or THERE EXISTS

y Both the universal and the existential can be either negative or affirmative



Graphical Depiction

y Understanding the logical processes in statement (worded) form can be

difficult

y Venn Diagrams can be used to help the reasoner understanding particular

situation

y Some properties:

o The circle denote sets of things/objects/people

o Shaded areas indicate that there are no elements or members

o An X denotes at least one member or element

o Consider the following argument:

1. All lecturers are human

2. All humans are mortal

3. @ All lecturers are mortal

y Premise 1 is represented by the grey shading,

whereas the yellow is premise 2



Compos sus Cat ori al St at ments

y So far we have been stu ing cat egorical st at ements

y These are st at ements about one particular thing (e.g. all lecturers are human)

y However, st at ements can be joined t ogether and even negat ed

y E.g.

o If the batt ery is flat , then the car will not st art o A s uare has four sides and a t riangle has 3 sides

o The Knowledge Societ y exam is on Monday or is it onTuesdayo The Knowledge Societ y exam is not an assessment it em

y Can evaluat e the t ruth of each of these st at ements

y Logicians have developed a syst em that can aut omatically evaluat e the t ruth composed st at ements

y Called t ruth f unction logic or simply symbolic logic

y It is used as the basis of all elect ronic comput ation

y Logicians assign st at ements variable names

y This makes the easier t o work with

y E.g.o A s uare has four sides and a t riangle has 3 sides becomes A^B,

where A = a s uare has four sides, ^ =AND, B = A t riangle has 3sides

y A logical operat or (such as AND) combines two or more simple st at ements

t ogether int o a compound st at ement

y The basic operat ors are:

y The operat ors can best be explained using t ruth t ables

y Consider a st at ement such as A = It is hot



y Evaluat e: A^BpA

y In the previous case we have a t aut ology, as all the out puts are t rue

y If the out puts are all false, we would have a cont radiction

y Consider A = It is Hot

o A~A is a cont radiction

o A~A is a t aut ology

y If we have a complex compound st at ement , we can evaluat e using t ruth t ables

y Boolean algebra can evaluat e these st at ements symbolically and underpins

the operations of all digit al comput ers

lecture 10 - reasoning with knowledge

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