Statement Logic
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What is inductive reasoning?
concerns inferences that will be true with some probability Ex.Bayes rule
What is deductive reasoning?
The truth of some statements or information guarantees some other statement must be true concerns inferences guaranteed to be true, given some premises (e.g., statement logic)
What is normative theories?
how people should behave
What are descriptive theories?
how people actually behave
What is logic?
The analysis and appraisal of arguments
Why study logic?
Provides a normative model of reasoning provides a model of meaning Builds AI that reasons effectively
When is an argument valid?
Whenever its premises are true, its conclusion must be true as well
When is an argument sound?
If it is valid and the premises are actually true
What does validity depend?
Depends on the form/structure of the argument
What is the structure for a valid argument?
[Premise 1] P OR Q [Premise 2] NOT P [Conclusion] Q
What is statement logic?
A formal language where the basic symbols stand for statements Statements can be combined via logical connectives, which are truth-functional It provides a mechanical means of determining what statements must be true given other statements
What are truth tables?
Tell you how the truth-value of a compound statement depends on the truth-values of components
When is an argument deductively valid?
When the truth of the premises would guarantee the truth of the conclusion
What is tautology?
Any statement that is true, no matter what the truth-values of its atoms
What is logical equivalence?
Two statements that have identical truth conditions- they mean the same thing