Meritorious Prof. Dr. S. M. Aqil Burney

Director UBIT Chairman

Department of Computer Science University of Karachi

burney@computer.org www.drburney.net

Designed and Assisted by

Hussain Saleem

hussainsaleem@uok.edu.pk

06th March 2008

"Well begun is half done"

--Aristotle, quoting an old proverb

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Research Methods

In research, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.

Research Types

Deductive Approach

Inductive Approach

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Deductive Research Approach

THEORY

HYPOTHESIS

OBSERVATION

Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. Conclusion follows logically from premises (available facts)

Waterfall

CONFIRMATION

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Inductive Research Approach

Inductive reasoning works THEORY the other way, moving from specific observations to broader generalizations TENTATIVE and theories. HYPOTHESIS Informally, we sometimes call this a "bottom up" approach Hill PATTERN Climbing Conclusion is likely based on premises. Involves a degree of uncertainty OBSERVATION 5

Deductive Vs. Inductive

THEORY THEORY

HYPOTHESIS

TENTATIVE HYPOTHESIS

OBSERVATION

PATTERN

CONFIRMATION OBSERVATION

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Deductive Vs. Inductive

Induction is usually described as moving from the specific to the general, while deduction begins with the general and ends with the specific. Arguments based on laws, rules and accepted principles are generally used for Deductive Reasoning. Observations tend to be used for Inductive Arguments. 7

Logical Reasoning and Human Nature

Historically, many researchers believed that logical reasoning is an essential part of human thought process and this dominates in scientific & Technological research and Development. However, humans are not natural logical reasoners REFERENCE:

S. M. Aqil Burney; Nadeem Mahmood, “A Brief History of Mathematical Logic Mahmood, and Applications of Logic in CS/IT”, Karachi University Journal of Science Vol.34 (1) July 2006. PP 61-75 61 CS/IT”

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Reasoning methods and Argumentation

The main division between forms of reasoning that is made in philosophy is between deductive reasoning and inductive reasoning. Formal logic has been described as 'the science of deduction'. The study of inductive reasoning is generally carried out within the field known as informal logic or critical thinking. 10

http://www.phac-aspc.gc.ca/publicat/cdic-mcc/18-3/d_e.html 11

Automated Reasoning

• Logic lends itself to automation. • A variety of problems can be attacked by representing the problem description and relevant background information as logical axioms and treating problem instances as theorems to be proved. 12

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Logic and Reasoning

Reasoning

Using given knowledge and truth value help us to solve, understand real life problems.

Logical Reasoning

Probabilistic Reasoning

Bayesian Networks

Subjective

Objective

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EXAMPLE

• • •

p: All mathematicians wear glasses q: Anyone who wears glasses is an algebraist r: All mathematicians are algebraist

p∧q → r ≡ ( ∼( p∧q) ∨ r)

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TRUTH TABLE

Truth Table for the formulae built with the Logical Operators

p T T T T F F F F

q T T F F T T F F

r T F T F T F T F

pΛq ~(pΛq) ~(pΛq)Vr Λ Λ Λ T F T T F F F T T F T T F T T F T T F T T F T T 15

If r is the conclusion, and we know that p and q are true simultaneously then r is valid statement. In real life, the statements are true or false, here statement means an atomic statement, thus statements may be simple (atomic) or component. If p, q and r are independent statements, then we need to prove: p∧q → r

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Commitment

Ontological Commitment: What exists in the world: Language of reasoning (Formal). Epistemological Commitment What an intelligent entity believes about the fact. Believe System: True, False,...

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