Meritorious Prof. Dr. S. M. Aqil Burney
Director UBIT Chairman
Department of Computer Science University of Karachi
Designed and Assisted by
06th March 2008
"Well begun is half done"
--Aristotle, quoting an old proverb
In research, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive Research Approach
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)
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
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”
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
• 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
Logic and Reasoning
Using given knowledge and truth value help us to solve, understand real life problems.
• • •
p: All mathematicians wear glasses q: Anyone who wears glasses is an algebraist r: All mathematicians are algebraist
p∧q → r ≡ ( ∼( p∧q) ∨ r)
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
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,...