Download presentation

Presentation is loading. Please wait.

Published byChrystal Patrick Modified over 5 years ago

1
Copyright © Peter Cappello Logical Inferences Goals for propositional logic 1.Introduce notion of a valid argument & rules of inference. 2.Use inference rules to build correct arguments.

2
Copyright © Peter Cappello What is a rule of inference? A rule of inference allows us to specify which conclusions may be inferred from assertions known, assumed, or previously established. A tautology is a propositional function that is true for all values of the propositional variables (e.g., p ~p).

3
Copyright © Peter Cappello Modus ponens A rule of inference is a tautological implication. Modus ponens: ( p (p q) ) q

4
Copyright © Peter Cappello Modus ponens: An example Suppose the following 2 statements are true: If it is 11am in Miami then it is 8am in Santa Barbara. It is 11am in Miami. By modus ponens, we infer that it is 8am in Santa Barbara.

5
Copyright © Peter Cappello Other rules of inference Other tautological implications include: (Is there a finite number of rules of inference?) p (p q) (p q) p [~q (p q)] ~p [(p q) ~p] q [(p q) (q r)] (p r) hypothetical syllogism [(p q) (r s) (p r) ] (q s) [(p q) (r s) (~q ~s) ] (~p ~r) [ (p q) (~p r) ] (q r ) resolution

6
Copyright © Peter Cappello Common fallacies 3 fallacies are common: Affirming the converse: [(p q) q] p If Socrates is a man then Socrates is mortal. Socrates is mortal. Therefore, Socrates is a man.

7
Copyright © Peter Cappello Common fallacies... Assuming the antecedent: [(p q) ~p] ~q If Socrates is a man then Socrates is mortal. Socrates is not a man. Therefore, Socrates is not mortal.

8
Copyright © Peter Cappello Common fallacies... Non sequitur: p q Socrates is a man. Therefore, Socrates is mortal. The following is valid: If Socrates is a man then Socrates is mortal. Socrates is a man. Therefore, Socrates is mortal. The argument’s form is what matters.

9
Copyright © Peter Cappello Examples of arguments Given an argument whose form isn’t obvious: Decompose the argument into premise assertions Connect the premises according to the argument Check to see that the inference is valid. Example argument: If a baby is hungry, it cries. If a baby is not mad, it doesn’t cry. If a baby is mad, it has a red face. Therefore, if a baby is hungry, it has a red face.

10
Copyright © Peter Cappello ( (h c) (~m ~c) (m r) ) (h r) r m c h

11
Copyright © Peter Cappello Examples of arguments... Argument: McCain will be elected if and only if California votes for him. If California keeps its air base, McCain will be elected. Therefore, McCain will be elected. Assertions: m: McCain will be elected c: California votes for McCain b: California keeps its air base Argument: [(m c) (b m)] m (valid?)

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google