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Published in:
2012 | OriginalPaper | Chapter
3. Propositional Logic: Deductive Systems
Author : Prof. Mordechai Ben-Ari
Published in: Mathematical Logic for Computer Science
Publisher: Springer London
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Abstract
The concept of deducing theorems from a set of axioms and rules of inference is very old and is familiar to every high-school student who has studied Euclidean geometry. Modern mathematics is expressed in a style of reasoning that is not far removed from the reasoning used by Greek mathematicians. This style can be characterized as ‘formalized informal reasoning’, meaning that while the proofs are expressed in natural language rather than in a formal system, there are conventions among mathematicians as to the forms of reasoning that are allowed. The deductive systems studied in this chapter were developed in an attempt to formalize mathematical reasoning.