LOGIC & TRUTH.pptx PROPOSITIONAL LOGIC AND ETC.

SEMANTICS

1. LOGIC & TRUTH SEMANTICS

2. Logic is like a set of rules for thinking and figuring things out. It's a way of using information to come to a sensible conclusion. Logic helps us sort through all of that and decide what to believe or accept as true. It's like a guide that tells us when an argument makes sense and when it doesn't. What is Logic?

3. EXAMPLE(S): 1. "All mammals have fur. Dogs are mammals. Therefore, ____ have ___,"

4. EXAMPLE(S): 1. "All mammals have fur. Dogs are mammals. Therefore, Dogs have fur." We're using logic to connect the dots and reach a reasonable conclusion based on what we know.

5. EXAMPLE(S): 1. "All mammals have fur. Dogs are mammals. We're using logic to connect the dots and reach a reasonable conclusion based on what we know. 2. “All humans are mortal. Marc is a _____. Therefore, ____ is _____. Therefore, Dogs have fur."

6. EXAMPLE(S): 1. "All mammals have fur. Dogs are mammals. We're using logic to connect the dots and reach a reasonable conclusion based on what we know. 2. “All humans are mortal. Marc is a mortal. Therefore, Marc is human. Therefore, Dogs have fur."

7. EXAMPLE(S): "All clouds are made of cheese. Cats like to sleep on clouds. Therefore, cats like to sleep on cheese."

8. EXAMPLE(S): "All clouds are made of cheese. Cats like to sleep on clouds. Therefore, cats like to sleep on cheese." This sentence lacks sense because it makes an illogical connection between clouds and cheese. What does it imply?

9. EXAMPLE(S): "All clouds are made of cheese. Cats like to sleep on clouds. Therefore, cats like to sleep on cheese." This sentence lacks sense because it makes an illogical connection between clouds and cheese. What does it imply? THE SENTENCE DOES NOT MAKE SENSE!

10. EXAMPLE(S): "All clouds are made of cheese. Cats like to sleep on clouds. Therefore, cats like to sleep on cheese." This sentence lacks sense because it makes an illogical connection between clouds and cheese. What does it imply?

11. EXAMPLE(S): "All clouds are made of cheese. Cats like to sleep on clouds. Therefore, cats like to sleep on cheese." This sentence lacks sense because it makes an illogical connection between clouds and cheese. What does it imply? "All clouds are made of marshmallows. Fish enjoy swimming in clouds. Therefore, fish enjoy swimming in marshmallows."

12. EXAMPLE(S): "All students who study hard get good grades. Sarah studies hard. Therefore, Sarah will likely get good grades." This sentence makes sense because it follows a logical structure.

13. TYPES OF LOGIC DEDUCTIVE, INDUCTIVE, & SYMBOLIC

14. DEDUCTIVE LOGIC Deductive logic is a way of thinking where if you start with true statements and use valid reasoning steps, you can guarantee the conclusion will also be true. (It's like following a recipe.) Deductive Logic: Conclusion necessarily follows from premises. WHAT DOES THIS MEAN?

15. DEDUCTIVE LOGIC Deductive Logic: Conclusion necessarily follows from premises. If the premises ( the initial statements or assumptions ) are true, and if the logical structure of the argument is valid, then the conclusion must also be true. This principle is known as the principle of deductive validity.

16. DEDUCTIVE LOGIC Deductive logic is a way of thinking where if you start with true statements and use valid reasoning steps, you can guarantee the conclusion will also be true. All mammals are warm-blooded. (True premise) EXAMPLE: A dog is a mammal. (True premise) Therefore, a dog is warm-blooded. Deductive logic is a way of thinking where if you start with true statements and use valid reasoning steps, you can guarantee the conclusion will also be true.

17. DEDUCTIVE LOGIC Deductive logic is a way of thinking where if you start with true statements and use valid reasoning steps, you can guarantee the conclusion will also be true. SCENARIO: Premise 1: The diamond necklace was last seen in the jewelry box. Premise 2: The jewelry box was found in the locked safe. Premise 3: Only the butler and the maid have access to the safe. Premise 4: The butler has an alibi for the time when the necklace went missing. Conclusion: Therefore, based on deductive reasoning, the maid must have taken the necklace. Let's consider a detective solving a mystery using deductive logic :

18. INDUCTIVE LOGIC Inductive logic is a form of reasoning where conclusions are drawn based on observed patterns. Inductive logic is like making an educated guess based on what you've seen before. It's when you use past experiences to make predictions about what might happen next. Reasoning from specific instances.

19. INDUCTIVE LOGIC Explanation: Imagine you have a bag of colored marbles, and you've pulled out ten marbles so far. All ten have been red. Using inductive logic, you might guess that the next marble you pull out will also be ___. Why?

20. INDUCTIVE LOGIC Explanation: Imagine you have a bag of colored marbles, and you've pulled out ten marbles so far. All ten have been red. Using inductive logic, you might guess that the next marble you pull out will also be ___. Why? Because based on the pattern you've observed so far, it seems likely.

21. INDUCTIVE LOGIC Example: Let's say you're a kid who loves ice cream. Every time you go to the ice cream shop, you notice that they have vanilla, chocolate, and strawberry flavors. Every time you've gone, you've picked chocolate. Using inductive logic, you might think that?

22. INDUCTIVE LOGIC Example: Let's say you're a kid who loves ice cream. Every time you go to the ice cream shop, you notice that they have vanilla, chocolate, and strawberry flavors. Every time you've gone, you've picked chocolate. (Using inductive logic, you might think that?) "Every time I've been to the ice cream shop, they've had chocolate. So next time I go, they'll probably have chocolate again." Based on your past experiences (inductive reasoning), you make a prediction about the future.

23. INDUCTIVE LOGIC Scenario: You've noticed that every time it rains, the streets get wet. So, when you wake up one morning and see dark clouds outside, you might use inductive logic to predict that it will rain today. It's not guaranteed, but based on your past observations, it seems likely.

24. SYMBOLIC LOGIC Symbolic Logic: Using symbols to represent logical relationships. Symbolic logic is like using a secret code to talk about ideas. Instead of using regular words and sentences, we use symbols to represent different parts of logical statements, like "and," "or," "not," and "if...then." Deals with representing logical relationships and operations using symbols.

25. SYMBOLIC LOGIC Symbolic logic is like using a secret code to talk about ideas. Instead of using regular words and sentences, we use symbols to represent different parts of logical statements, like "and," "or," "not," and "if...then."

26. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (IF...THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella."

27. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (IF...THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining."

28. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (IF...THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining."

29. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (IF...THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining."

30. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining." 3.) (P→Q) ∧ (¬Q→¬P) 4.) (¬P∧¬Q)∨(P∧Q) 5.) (P∧Q)↔(Q∧P)

31. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining." 3.) (P→Q) ∧ (¬Q→¬P) "If it is raining, then I am using an umbrella, and if I am not using an umbrella, then it is not raining."

32. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining." 3.) (P→Q) ∧ (¬Q→¬P) "If it is raining, then I am using an umbrella, and if I am not using an umbrella, then it is not raining." 4.) (¬P∧¬Q)∨(P∧Q)

33. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining." 3.) (P→Q) ∧ (¬Q→¬P) "If it is raining, then I am using an umbrella, and if I am not using an umbrella, then it is not raining." 4.) (¬P∧¬Q)∨(P∧Q) "It is not raining and I am not using an umbrella, or it is raining and I am using an umbrella."

34. SYMBOL MEANING P It is raining. Q I am using an umbrella. ∧ Conjunction (AND) ∨ Disjunction (OR) ¬ Negation (NOT) → Implication (THEN) ↔ Equivalence (IF AND ONLY IF) SYMBOLIC LOGIC 1.) P∧Q Represents "It is raining AND I am using an umbrella." 2.) ¬P Represents "It is NOT raining." 3.) (P→Q) ∧ (¬Q→¬P) "If it is raining, then I am using an umbrella, and if I am not using an umbrella, then it is not raining." 4.) (¬P∧¬Q)∨(P∧Q) "It is not raining and I am not using an umbrella, or it is raining and I am using an umbrella." 5.) (P∧Q)↔(Q∧P) "It is raining and I am using an umbrella if and only if I am using an umbrella and it is raining."