Wednesday, October 10, 2012

Introduction to Logic @ FIX University Cultural Campus


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More FIX on the NET @ FIX University Cultural Campus

Welcome to Spring Semester 2013

Fernando IX University
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Fernando IX University


Introduction to Logic


Michael Genesereth, Associate Professor

In this course, you will learn how to formalize information and reason systematically to produce logical conclusions. We will also examine logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.
Fernando IX University

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Week 3

That's two weeks behind us. Six weeks to go. By this point, you should all be familiar with the syntax and semantics of Propositional Logic. You should familiar with the concepts of satisfiability, validity, and logical entailment. In fact, you should be more than familiar with this material - ideally, you should be saying to yourself (and others) that, when all is said and done, this stuff is pretty easy. In fact, it *is* easy. And it should be. There is more difficult material to come; but hopefully, after we have gone through it all, you will think that that is easy too!

Once again this week, the Forum was a lively place. We were pleased to see so much discussion about the exercises and problems, with some people asking questions, some people providing answers, some people arguing that our answers are wrong (they are not), and others defending them. Last week, I mentioned Mike Malveaux's efforts to help others; this week, I was particularly struck by the helpful answers of Alison Perera, Nuno Miguel Brito Nogueira, Antonia Bustamante, and others.

On a personal note, I would also like to thank those of you who have posted supportive messages. And those of you who have posted details about your circumstances and reasons for taking the course. I was particularly struck by the message posted by Jeanette Schroeder, a Peace Corps volunteer serving in Ecuador. There are a lot of benefits to producing online courses; but getting messages like that is one of the best.

This coming week, we finally get to logical reasoning - rules of inference, proofs, and so forth. We look at several different proof systems. Lesson 3 covers the Mendelson proof system and the Fitch proof system. Lesson 4, which is optional, covers Propositional Resolution. Lesson 5, which is also optional, provides more detail on checking satisfiability and validity. By the time you are done this week, you should be comfortable doing proofs in Propositional Logic; and you should be ready to opine about the relative merits of the various systems - praising one and dissing another.

This week, we are releasing the final version of the video and notes for Lesson 3, and we are releasing the video and notes for the **optional** Lessons 4 and 5. There is also a new puzzle. This one is relatively easy, but there are some really challenging ones coming.

By the way, we will be releasing answers and explanations for the problems associated with each lesson as soon as the hard deadline has passed. And we hope to have more practice exercises for you in the weeks to come.

After this week, we will begin our discussion of Herbrand Logic. However, we are not providing a preview, as we want you to get really comfortable with Propositional Logic before we embark on that part of our journey. If you really want something to do, study the material in Lessons 4 and 5.

We have received a few complaints about technical difficulties with some of the exercises and problems. These are mostly browser and/or platform incompatibilities. Sorry for any trouble you may have encountered. We are working with the Coursera folks to resolve these problems. Please be patient. And let us know if you think there is a technical problem.

One final note. For those of you who are bothered by our policy of allowing only one attempt at homework problems, we are working on the concept of make-up problems. Under this proposal, you would get to take the higher of your scores on the original problems or the make-up problems. So, if you messed up on the original problems, you may get another chnace. Stay tuned for more details as we develop this idea.

mike
Mon 8 Oct 2012 12:00:00 PM PDT

Week 2

One week down, seven to go. (Yes, the course is eight weeks long, not seven as listed on the site.) All we have covered is the Introduction, but it seems as though we have already done a lot. And, in a way, we have - we have already touched on all of the main topics of the course - syntax and semantics, logical entailment and reasoning, formalization and automation.

Judging by the discussion on the Forum, it appears that, for many of you, the toughest part of the problem set was figuring out how to find models for sentences. In the weeks to come, we will see ways to systematize this process. The point in giving you these problems was twofold. (1) We wanted you to understand the distinction and relationship between sentences and the "worlds" that satisfy those sentences. (2) We wanted you to appreciate the value of reasoning as opposed to blind enumeration. It is not practical to consider 65,536 possible worlds. However, these problems can be solved without such enumeration by reasoning about the sentences. In a comment on this in the Forum, I gave an analogy to Sudoku. While it is, in principle, possible to solve any Sudoku puzzle by exhaustive enumeration, this is impractical. The point is to use reasoning to solve such puzzles.

By the way, we were especially happy to see so much discussion in the Forum. We applaud those of you who took advantage of the Forum to ask questions, and we appreciate those of you (Michael Malveaux and others) who spent time answering these questions. Also those of you who shared your perspectives on open questions, puzzles, and so forth. (Kudos to Edward Jackman for a particularly elegant explanation of the solution to the Coins puzzle.) We are grateful to those of you who reported bugs and made suggestions on how to improve the videos and notes. And those of you who introduced yourselves and shared your reasons for taking the course. And especially those of you who shared your jokes. (Credit to Varun Pant for getting this started.)

Now, with the introduction behind us, it is time to get down to serious work. This second week, your goal is to master the material in Lesson 2. You should learn the syntax and semantics of Propositional Logic; you should understand the notions of satisfiability and validity and logical entailment; and you should understand how to compute these properties for Propositional Logic.

This week, we are releasing the videos Lesson 2. You already have the notes (Chapter 2). We are also releasing a new set of problems. Look for more exercises on the Exercises page. (Remember that these are just duplicates of the exercises in the videos, and they do not count toward your grade.) Finally, for your edification and entertainment, there is a new puzzle - Logicians.

Next week, we will see how to do proofs for Propositional Logic; and, for those of you who want to go deeper, there will be several optional lessons for you to master. In week 4, we will start in on Herbrand Logic, which is quite a bit more challenging (and more useful) than Propositional Logic. And in week 8, we will look at First Order Logic - the classic logic taught in traditional Mathematical Logic courses. And stay tuned for upcoming special features - field trips, logic games, and a short somewhat irreverent piece on the making of the course.

Mike and Eric

PS: Click here for a logic cartoon / hint for this week's puzzle.
Mon 1 Oct 2012 12:00:00 PM PDT

Week 1


Okay. We are on our way! First week of class begins now.

This week, your goal is to master the material in lesson 1. This should not be too hard. The lesson is mostly overview. That said, you should not shortchange the material. This lesson talks about the main ideas of Logic and how they relate to each other, and it provides a framework for organizing the rest of the material in the course. This week, you should also master the art of doing interactive exercises and doing the online problems. You should check out the Puzzles, and you should figure out how to use Discussion Forums.

Mike
Mon 24 Sep 2012 12:00:00 AM PDT

Welcome!

We are happy to have you join us for this introductory course on Logic. We have been teaching logic for many years, but this is only the second time we are offering the course in this online format. We believe the online format has potential for improving logic education and for bringing the material to a wide audience.

The course consists of eight primary lessons on different aspects of Logic. Each lesson consists of several sections, each with its own video and notes and exercises, and there is one problem set per lesson. Our intent is to proceed through one lesson per week, which means you need to view 1-2 hours of video and do one problem set each week.

In addition to these primary lessons, the course contains auxiliary lessons, puzzles, and ancillary readings for those of you who want to explore beyond the primary material of the course. This material is not required. However, you are encouraged to look at these materials as they reinforce and extend the course in interesting ways.

The course begins officially on September 24. You should study the first lesson during the first week and do the problem set by the end of the week. That said, we do not care so much about deadlines; we care more that you get through the material.

Importantly, you should take advantage of the discussion forums to communicate with your fellow students and with the instructors. Use the forums to ask questions, answer questions, and add additional material to the course.

We hope the course will be a rewarding, educational, and entertaining experience for you. We are sure that it will be a learning experience for us; and we are looking forward to working with you.

Mike and Eric
Sun 23 Sep 2012 12:00:00 AM PDT

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