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Chapter 2
- LOGIC THINKING
Logical thinking is the process in which one uses
reasoning consistently to come to a conclusion.
The basic of all logical thinking is sequential thought.
This process involves taking the important ideas, facts
and conclusions involved in a problem and arranging
them in a chain like progression that takes on a meaning
in and of itself
To think logically, is to think in steps
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What Is Logic ?
Logic is a way to describe situations or knowledge.
It is useful in A.I. because we need to represent the problemswe
want to solve.
Logic, unlike natural language is precise.
For example: "Every man loves a woman"
Which woman? One unique to each man? The same woman?
In logic: ForAll(M) For Some(W) [ man(M) -> woman(W) and
loves(M,W)] means: "Every man has at least one woman who they
love"
For some, logic unlike natural language is hard to read
andunderstand.
But we need to be precise in a computer program.
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Are We Logical
You have 4 letters
The letter is either sealed or open The stamp is either premium
(40) or standard
price (30)
You have these letters
Which ones do you turn over to test the rule:
"If a letter is sealed then it must have apremium stamp (40) on
it"
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EXAMPLE OF LOGIC
All students are poor
Jo is a student
So we can infer that Jo is poor
Notice that if we make wrong statements about our
'world' the inference is likely to be wrong.
Logic assumes that all statements made are true, sothat we can
rely on the inferences only if they really
are true statements
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What is Good about Logic?
It is precise.
It allows inference to establish new relationships
from old.
It allows programs to be written which aredeclarative - they
describe what is true and not howto solve problems.
Problems are solved by general purpose inferencerssuch as
Prolog's resolution refutation
Further
readinghttp://philosophy.hku.hk/think/logic/whatislogic.php
http://philosophy.hku.hk/think/logic/whatislogic.phphttp://philosophy.hku.hk/think/logic/whatislogic.php
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Types of Logic
Propositional logic
All objects described are fixed or unique
"John is a student" student(john) Here John refers to one unique
person.
First order predicate logic
Objects described can unique or variables to stand for a
uniqueobject
"All students are poor"
For All(S) [student(S) -> poor(S)]
Here S can be replaced by many different unique students.
This makes programs much more compact:
eg. For All (A,B) [brother (A,B) -> brother (B,A)] replaces
half thepossible statements about brothers
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FALLACIES
Fallacies are mistakes of reasoning, as opposed to
making mistakes that are of a factual nature. The
study of fallacies is an application of the principles of
critical thinking. Being familiar with typical fallacies
can help us avoid them. We would also be in a
position to explain other people's mistakes.
EG: If I counted twenty people in the room whenthere were in
fact twenty-one, then I made a factual
mistake.
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FOUR KINDS OF FALLACIES
Fallacies of inconsistency are cases where somethinginconsistent
or self-defeating has been proposed or accepted,
as in believing in the existence of round squares. Fallacies of
inappropriate presumption are cases where we
have an assumption or a question presupposing something thatis
not reasonable to accept in the relevant conversationalcontext.
Fallacies of relevance are cases where irrelevant reasons
are
being invoked or relevant reasons being ignored. Fallacies of
insufficiency are cases where the evidence
supporting a conclusion is insufficient or weak. The
naturalisticfallacy is one example.
http://philosophy.hku.hk/think/fallacy/ic.phphttp://philosophy.hku.hk/think/fallacy/ip.phphttp://philosophy.hku.hk/think/fallacy/ir.phphttp://philosophy.hku.hk/think/fallacy/is.phphttp://philosophy.hku.hk/think/fallacy/is.phphttp://philosophy.hku.hk/think/fallacy/ir.phphttp://philosophy.hku.hk/think/fallacy/ip.phphttp://philosophy.hku.hk/think/fallacy/ic.php
