CS 210: Mathematical Logic Notes
words premises::假设，前提
words entails::合乎逻辑的推理
words evaluation criteria::评估标准
words Axiom::公理
words Theorem::定理
words Lemma::引理
words Proof::证明
words Syllogism::三段论
- 三段论
- Truth(正确性) for statements, Validity(有效性) for arguments/reasoning. They are not the same.
words proposition::命题
words deduction::推理
words derivation::导出
Formula languages::形式语言
Formula languages : a precisely defined set of symbols and syntax(句法) rules.Using symbols and apply syntax rules to form formulas, where formulas represent propositions.
Formula Deduction System::形式推演系统Formula Deduction System
logical truth or falsity(错误) of propositions is expressed through deductive calculations based on the formulas and rules.Alphabet(字母):Symbols logical operators(And, Or, NOT, etc.),predicates,断言, constants, variables, and quantifiers(量词)
Syntax(句法): What makes a valid formula
Semantics(含义): Truth values and meanings for formulas.
Deduction systems(推理系统) : rules for performing deduction.
