Question ONE There are some principles and rules guiding the reasoning process. Can we specify them in a They are mathematical independent with way? the facts/contents we are reasoning about
Question ONE Can we specify them in a mathematical way? There are some principles and rules guiding the reasoning process. They are independent with the facts/contents we are reasoning about
Formalization 勉 WHY Precise Effective Correct Description Reasoning Proving do we need How to How to carry out What is a correct unambiguously reasoning? proof? formalization? specify a statement
Formalization WHY do we need formalization? How to unambiguously specify a statement. Precise Description How to carry out reasoning? Effective Reasoning What is a correct proof? Correct Proving
Formalization Proposition Proposition Variable Logic Connectives Fundamental Logic Logic Formulas Logical Equivalence Elements Predicate Inference Quantifier
Formalization Fundamental Logic Elements ► Proposition & Proposition Variable ► Logic Connectives ► Logic Formulas ► Logical Equivalence ► Predicate & Quantifier ► Inference
Proposition(命题) A proposition/statement is a sentence that is true or false (might be unknown),but not both My salary of this month is greater than that of last month. Today is Tuesday,and it is raining. Can you speak English? 3-x=5 Every even integer greater than 2 can be expressed as the sum of two primes "What I'm talking now is fake." paradox
is a sentence that is true or false (might be unknown), but not both Proposition（命题） A proposition/statement My salary of this month is greater than that of last month. Today is Tuesday, and it is raining. Can you speak English? 3-x=5 Every even integer greater than 2 can be expressed as the sum of two primes “What I’m talking now is fake.” paradox
Proposition Variable(命题变元) Usually,we use lower case letters to denote proposition variables (e.g.,p,q,r) ·p:Today is Friday ·q:2+2=4 ·r:Bill is from Boston ·The range of a proposition variable:{T,月 p:Today is Friday(p=F) ·q:2+2=4(q=T) r:Bill is from Boston (r=F)
Proposition Variable（命题变元） • Usually, we use lower case letters to denote proposition variables (e.g., p, q, r) • p : Today is Friday • q : 2+2=4 • r : Bill is from Boston • The range of a proposition variable: {T, F} • p: Today is Friday (p=F) • q: 2+2=4 (q =T) • r: Bill is from Boston (r=F)