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# Introduction to Formal Logic PowerPoint PPT Presentation

Introduction to Formal Logic. CSC 333. Why isn’t English a programming language?. Ambiguity! Words with double meanings. Meanings of clauses depend on Punctuation Spoken emphasis Context Order of words Lack of precision And so forth. Formal Logic. Eliminates ambiguity.

Introduction to Formal Logic

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## Introduction to Formal Logic

CSC 333

### Why isn’t English a programming language?

• Ambiguity!

• Words with double meanings.

• Meanings of clauses depend on

• Punctuation

• Spoken emphasis

• Context

• Order of words

• Lack of precision

• And so forth

### Formal Logic

• Eliminates ambiguity.

• Provides a means of conveying information clearly.

• Uses capital letters to represent statements. For example, A could represent “CSC 333 is fun” and B could represent “CSC 333 is easy.”

• Uses logical connectives to connect statements.

• Λ means “and”.

### Is A Λ B true?

• If CSC 333 is indeed fun and CSC 333 is easy, then we could agree that A Λ B is true.

• If CSC 333 isn’t fun, but it’s easy, is A Λ B true?

• If CSC 333 is hard, but it’s fun, is A Λ B true?

• If CSC 333 is boring and you can’t pass it, is A Λ B true?

### Is A Λ B true?

• A Λ B is true only when A is true and B is true.

• The truth value of A Λ B really depends on whether the truth value of A and the truth value of B, which can vary depending on the student, the teacher, the book, and other variables.

• We can show the situations that determine the truth or falsity of A Λ B in a truth table.

### Is A Λ B true?

• A truth table should contain all possible combinations of truth values for its statement letters.

• For example,

AB

tt

tf

ft

ft

### Is A Λ B true?

• We can see that all possible combinations of truth values are represented.

AB A Λ B

ttt

tf f

ft f

ft f

• The table shows what we already know! That A Λ B is true only when both A is true and B is true.

### Terms

• Proposition

• A statement (basic logical component) that is either true or false.

• Logical connective

• Binary - Logical operator connecting propositions.

• Conjunction (and); disjunction (or); implication (if-then); equivalence (is the same as).

• Unary – Logical operator acting on one logical component.

• negation (not).

• Compound statement

• A statement composed of multiple propositions connected by logical connectives.

### More terms

• Antecedent

• Consequent

• wff – well-formed formula

• Tautology

• Hypothesis

• Algorithm

### Truth tables

• Each row in a table shows a unique combination of truth values.

• A truth table must contain all possible combinations of truth values.

• A table with n statements must have how many rows?

• 2n

### Truth tables

• Consider the truth table on page 7.

• Note that there are 2 statements and, thus, 22 rows.

• Also, note the role that precedence plays in interpretation of the wff.

• In English, how can we summarize this situation? When is the wff true?

### To be continued . . .

• Notable terms:

• Modus ponens

• Modus tollens

• Valid argument

• Equivalence rules

• De Morgan’s laws

• Hypothetical syllogism

• Quantifiers