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Vacuous Truth
Приєднався 14 сер 2020
Hi, I'm Patrick, and I'm a recent Computer Science graduate. In these videos I aim to help you build an intuition for core parts of logic which are often taken for granted elsewhere.
6. Examples - Logic for Beginners
This final video in the Logic for Beginners series presents some examples. We first look at a toy example by using propositional logic to model and solve a "real world" problem. We then go on to look at an industrial strength logic called ACL2.
• Previous video: ua-cam.com/video/Qdi6k9kDUw0/v-deo.html
• Logic for Beginners playlist: ua-cam.com/play/PLXdZLVVi1lxXUcCUX4epFGTruqGKdpEw3.html
Additional Notes:
• 04:42 - To be clear, the bi-implication "A iff B" is true when both A and B are true or when both A and B are false. It may help to draw out a truth table!
• 10:39 - by "programs" I am referring to computer programs.
• 17:22 - when we talk about bi-implication we say "if and only if", which is shortened textually to "iff".
• 18:36 - "deterministically" here means that given a propositional formula ACL2 can always tell us whether it is true or false.
• 26:04 - The symbol "⊆" represents subset. So "X ⊆ Y" means "X is a subset of Y"
• 27:14 - the name "subset-reflexive" that is typed in is simply a name we give the theorem, it has no meaning internally and it simply helpful for humans.
• 28:19 - A list of some interesting applications of ACL2: www.cs.utexas.edu/users/moore/acl2/v8-3/combined-manual/index.html?topic=ACL2____INTERESTING-APPLICATIONS
00:00 - Introduction
00:57 - Propositional Example Scenario
05:36 - Propositional Proof
10:26 - ACL2 Overview
13:53 - Necessary Lisp Syntax
16:26 - Simple ACL2 Example
21:27 - More Complex ACL2 Example
27:40 - Industrial Uses of ACL2
28:23 - Conclusion
• Previous video: ua-cam.com/video/Qdi6k9kDUw0/v-deo.html
• Logic for Beginners playlist: ua-cam.com/play/PLXdZLVVi1lxXUcCUX4epFGTruqGKdpEw3.html
Additional Notes:
• 04:42 - To be clear, the bi-implication "A iff B" is true when both A and B are true or when both A and B are false. It may help to draw out a truth table!
• 10:39 - by "programs" I am referring to computer programs.
• 17:22 - when we talk about bi-implication we say "if and only if", which is shortened textually to "iff".
• 18:36 - "deterministically" here means that given a propositional formula ACL2 can always tell us whether it is true or false.
• 26:04 - The symbol "⊆" represents subset. So "X ⊆ Y" means "X is a subset of Y"
• 27:14 - the name "subset-reflexive" that is typed in is simply a name we give the theorem, it has no meaning internally and it simply helpful for humans.
• 28:19 - A list of some interesting applications of ACL2: www.cs.utexas.edu/users/moore/acl2/v8-3/combined-manual/index.html?topic=ACL2____INTERESTING-APPLICATIONS
00:00 - Introduction
00:57 - Propositional Example Scenario
05:36 - Propositional Proof
10:26 - ACL2 Overview
13:53 - Necessary Lisp Syntax
16:26 - Simple ACL2 Example
21:27 - More Complex ACL2 Example
27:40 - Industrial Uses of ACL2
28:23 - Conclusion
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5. Soundness and Completeness - Logic for Beginners
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This video in the Logic for Beginners series looks at two important concepts in logic, soundness and completeness. These are properties of a logic which tell us how the propositions which can be inferred using a deductive system relate to the semantics. We also take a brief excursion into Gödel's Incompleteness Theorem. • Previous video: ua-cam.com/video/-Vfd6AIZYFw/v-deo.html • Logic for Begin...
4. Deductive Systems - Logic for Beginners
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This video in the Logic for Beginners series explains the role of deductive systems in logic. As in previous videos, a general overview is given first: we look at some sentences in Propositional Logic that evaluate to True under any interpretation of the symbols. This motivates the explanation of a deductive system called Natural Deduction for Propositional Logic, and examples of its use are gi...
3. What is Syntax - Logic for Beginners
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This video in the Logic for Beginners series looks at the role of syntax in logic. We start off by looking at the role syntax plays in general before going onto the specific example of syntax in Propositional Logic. Additional Notes: • 11:35 - As a clarification, brackets exist to indicate structure which we are otherwise unable to show in concrete syntax. • 13:01 - The brackets in the proposit...
2. What is Semantics - Logic for Beginners
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This tutorial explains the role of semantics in logic and looks at how the semantics represent certain elements of the real world. The extended example of Propositional Logic is used again. The truth tables which define its semantics are used to explore some of the issues in an intuitive way, specifically looking at the definition or OR, and the notion of 'vacuous truth' as design choices. • Pr...
1. What is Logic - Logic for Beginners
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This video introduces the Logic for Beginners tutorial series. The series aims to answer the question "what is a logic?" from the perspective of an undergraduate student beginning to study the subject. I aim to give some insight I wish I had developed earlier. All logics comprise a syntax, a semantics and a deductive system and each of these concepts is developed in future videos. I also show a...