We are done. For real this time. Nothing more to come. Nothing. Rien. Nada. Except for certificates, of course. As soon as the hard deadline for the last set of problems has passed (16 December), we will compute grades for the class, and we will distribute certificates shortly thereafter.

The Coursera materials will remain accessible to you for several months. If I had my way, they would be accessible forever. As a small step in this direction, we are putting the Notes (with embedded exercises) and the Tools on our own website, and these are permanent. See below for link.

http://logic.stanford.edu/intrologic/

For those of you who cannot get enough logic, we will be back with a course on Logic Programming. We will email you all when it is ready. And don't forget the upcoming MOOC on General Game Playing, which will be held next Spring. Registration will open early in the new year. See the link below for more information.

https://class.coursera.org/ggp-004

We began this course by making public all of the notes and interactive exercises for Stanford's course on logic. Over the years, we have improved these somewhat with the help of students like you. Obviously, there is a lot more to be done. If you have specific suggestions on how to improve the course, please feel free to send me suggestions (email: genesereth@stanford.edu). (Suggestions other than having Anton take over as instructor, that is.)

Also, the administrators at Stanford would like to find out more about your experiences in taking the course. To this end, they have created a short post-course survey for you. Please click here to take take the survey. Thank you.

Finally, I just wanted to thank all of you who participated in the forum (e.g. Anton, Purgy, Athena, Tatiana, Antonio, John, and others). There is only so much one can teach in the form of videos and notes and hypercards and exercises; beyond that, students often need person-to-person help, and I know that many students benefited from the help of others. Hopefully, those of you who helped learned something in the process; and, in any case, you did a good thing. People helping others, no matter who, no matter where, for free - that is the real spirit of MOOCs.

mrg and christina and mikaela

Your friendly staff is back from the Thanksgiving break. Hopefully, you have had a good break yourselves. Or possibly you have been working diligently on those Induction proofs. Either is good.

And with that, we are finally done. Those of you who made it this far should feel pretty good - you have seen a lot of material, covered more rapidly and at a deeper level than in most other courses in Logic.

Well, I said we are done, but not quite. This week we are releasing a few additional videos with optional material. There is a video on the handling of equality in Relational Logic. There is a video on First-Order Logic and its relationship with General Relational Logic. And there is a video on General Game Playing, an unusual but interesting use of Logic. (For those of you who want to learn more about General Game Playing, there is Coursera course that will be offered in Spring 2016.)

https://www.coursera.org/course/ggp

Also, for those of you who started the course late or just did not manage to get all of the problems done on time, we have an early holiday present - we are changing the deadlines (soft and hard) for all problems to be 9 December 2015. This means that you still have a chance to get those problems done before we compute final grades and award certificates.

After the new hard deadline, we will make solutions to all exercises available via the notes. We will also release administrative details about the course, including average grades, certificates (with and without distinction), and so forth.

mrg and christina and mikaela

It is Thanksgiving week in the US. Time to step back and think about all of the good things in life - the things for which we are grateful and the things we might do to help others in return. Real significance - no work on the course this week. Unless, of course, you want to spend some time working on more proofs. Great way to have fun with friends and family! We will be back again next week with some extra material and a final wrap-up. Happy Thanksgiving.

mrg and christina and mikaela

We have almost completed our look General Relational Logic. We have seen the syntax and semantics of the language, and we have seen a couple of different proof systems - one based on Fitch rules and one based on Resolution and Factoring.

However, we are not quite done. While Fitch and Resolution, as we have seen them, are complete for Relational Logic, they are are not complete for General Relational Logic. We still need to deal with a type of reasoning that does not arise in Propositional Logic, viz. induction. We will spend the entire week looking at induction of various sorts.

As usual, we are releasing a new set of videos and notes and hypercards and exercises. The last two proofs are lengthy, so we have made the solutions accessible via the Notes. However, you must still do the exercises to get credit for them. As usual, there is a new puzzle, our final one, appropriately entitled Enlightenment. Not so difficult as Chessboard and a fitting last puzzle for the course.

After this week (and after the US Thanksgiving week that follows), we will look at some extra topics. And then, we will be done.

Finally, I wanted to say once again how pleased I am with the discussion on the Forum. Your efforts have helped us to correct various typos in the notes and on the hypercards. Many of you have helped others to understand the materials better. And there has been some interesting discussion about extensions to the material of the course, in one case (existential elimination) leading us to opt for a different definition in future offerings of the course. Thanks to everyone for your efforts, especially Anton and Tatiana and Purgy and John and Ad and others. And an extra special thanks to Athena for creating pdfs for the slides used in the lectures. Good citizens all. It is great to have you taking the course.

By now, we have seen the majority of the material of the course, most of the material that is taught in many introductory logic courses. And we have looked at the material at a deeper and more rigorous level than in most introductory courses. Congratulations to those of you who have stuck with it this far.

This week, we are releasing a lesson on resolution theorem proving for Relational Logic. Relational Resolution is a streamlined proof system analogous to Propositional Resolution. It is easier to use than Fitch, and it is ideal for automation. However, the proofs are not always as intuitive as with Fitch. That tradeoff between simplicity and intuitiveness of the resulting proofs is why we still use both systems.

As usual, there are videos, hypercards, notes, and exercises for your educational pleasure. And, as usual, there is a new puzzle, entitled Chessboard. It has some elements in common with the Cards puzzle. However, this one is more difficult, so don't be worried if you don't get it right away. (Some people have reported spending months on the problem.) The good news is that there is a simple and elegant solution (simple once you find it, that is). Good luck.

mrg and Christina and Mikaela

We have finally begun our discussion of Relational Logic (and General Relational Logic). Relational Logic is definitely more complex than Propositional Logic, but it is also more useful. Useful in thinking and communicating and interacting with logic-enabled Computer Systems (some of which as we shall see in the weeks to come).

This week, we begin our look at proofs in Relational Logic. Based on the message traffic about Propositional Logic proofs, I think I can say with confidence that at least some of you have found that generating proofs is not easy. Exactly so. Proving things, even very simple things, can be difficult. It depends on the proof system. What is easy in one system is often difficult in another and vice versa. There is no best proof system for all problems. One thing you should take away from these proof exercises is that finding proofs is a process of search in a space of possibilities. Another is a growing sense of confidence that everything that is true *can* be proved (albeit with some difficulty). And perhaps a belief that this search process can be automated (which by and large is correct).

As usual, there are videos, hypercards, notes, and exercises for your educational pleasure. And, as usual, there is a new puzzle, entitled Safecracking. And, if you just cannot get enough of proofs, take heart. At the end of the course, we will tell you about a website for finding and recording proofs. Stay tuned for more information on this website - on how you can use it and how you can contribute.

Note that Wednesday is the hard deadline for solutions to the proof problems in Chapters 4 and 5. After this, you will be able to find solutions to all of those problems by going to the Notes tab and clicking on the corresponding exercises at the ends of the chapters. After Wednesday, there will be a Show Answer button on all exercises that you can use to see the solutions. Going forward, there will be a similar button on some proof exercises (but not all) even before the hard deadline.

Finally, we just wanted to say once again how much we appreciate all of the discussion in the Forums. It is a great way to get help when you are stuck, and helping others is a great way to solidify your understanding of the material. Special thanks to Anton and Jose and Tatiana and Athina and John and Purgy for being extra good citizens.

mrg and christina and mikaela

Halfway through the course and the end of our treatment of Propositional Logic. Propositional Logic is simple and elegant. It has limitations, but it also has many applications. It is pedagogically valuable in that it provides us with a simple setting in which to look at the main concepts of Logic - syntax and semantics, validity and contingency and unsatisfiability, logical entailment, and proofs. In the weeks ahead, we will be revisiting these concepts in the context of a more complicated logic, and it will be good that we have already examined these concepts in this simpler setting.

As in past weeks, the Forum this week was once again very active. We do not always respond to comments ourselves (when we think others can help), but you can be sure that we read every single comment, whether or not we respond.

This coming week, we begin our look at Relational Logic and General Relational Logic. These logics are more expressive than Propositional Logic, and they have more practical uses. For some, the material may be a bit more difficult. It is conceptually the most difficult material in the course. It is the most difficult material in the course. It is definitely the most difficult material in the course. (Have we said that already?) Start early; don't wait till the end of the week. Read the notes. Do the exercises. And take advantage of the discussion forum to talk about things you find confusing and to help others understand the material.

The presentation of the this week's material is different from the corresponding presentation in previous versions of the course, and the notes differ from the text in the printed book. The material is the same, but we are experimenting with a different way of presenting it. In effect, we have split the material of the previous Chapter 6 into two Chapters - a new Chapter 6 that presents Relational Logic and a new Chapter 7 that adds functions to our language resulting in an extended version called General Relational Logic. We believe that you will find this easier than the previous version.

One result of this revision to the presentation is that the old videos are no longer appropriate. Rather than shoot new videos, we have decided to try presenting the material in the form of "hypercards", textual snippets corresponding ore or less to slides in the original videos. We have not finished our work on this transformation (as will be obvious at various points), but the material is complete and our tests have shown that this is a more effective presentation than the original videos.

If you do not like the hypercards, read the notes. The presentation in the notes is clearer than in the past, and there are more examples. There are also more extras this week, and we highly recommend that you take a look (especially the article on Model Building). And, as usual, there is a new puzzle.

After this week, the workload will get a little lighter, though the level of sophistication of the material from here on out is higher than that in the first few weeks. Next week, we will look at Relational Logic proofs. We will then look at the resolution method for Relational Logic. And after that we will look at proofs by induction.

mrg and Mikaela and Christina

Phew. Not an easy week. Especially for those of you seeing formal proofs for the first time. The good news is that, once you get the hang of it, doing proofs becomes a lot easier. Moreover, you can take comfort in knowing that our proof methods are sound and complete. If you manage to find a formal proof of a conclusion, the conclusion *must* be logically entailed; there can be no mistake. Also, if a set of premises logically entails a conclusion, it is always possible to find a formal proof of that conclusion.

A word about the Fitch system used in the course. The rules in this system are easy to use (though it is not always easy to know which ones to use to get a particular result). This contrasts with other systems where just figuring what the rules do is difficult. We chose this version because we thought it would help you learn about the methods, the difficulties, and the joys of doing proofs (when you finally succeed). The system can easily be elaborated with lots of additional rules of inference, making it a lot easier to use on practical problems. There is even a version that supports user-generated rules and meta-theorems, which make it possible to re-use earlier proofs when trying to prove more complicated results. But, before giving you these power tools, we want you to understand the basics.

This week, we look at another proof system - Propositional Resolution. Like Mendelson and Fitch, Propositional Resolution is sound and complete for Propositional Logic, i.e. everything that is provable is logically entailed and everything that is logically entailed is provable. However, Propositional Resolution is much simpler to use than these other proof systems, and proofs are frequently shorter than proofs in Mendelson or Fitch. For example, given p|q and ~p, it takes multiple steps or so to prove q in Fitch, whereas this can be done in 1 step in Propositional Resolution. That said, some people criticize Propositional Resolution because the proofs are sometimes less intuitive than Fitch proofs. Chacun a son gout. You will either love it or hate it. In any case, it is particularly useful for automating theorem proving - computers love it! And, by the way, it is equivalent to the simple rule of inference we looked at in the Introduction.

As usual, we are releasing videos and notes and problems about Resolution. (Sorry that the Box Logic video is out of focus. We will redo that video some day.) There is also a new puzzle. This one is a little more difficult than the previous puzzles. However, the course problems this week are not that difficult, so you will have more time to spend thinking about it.

mrg and Mikaela and Christina

Beginning of Week 3. By this point, you should have mastered the material in the first three lessons. In particular, you should now thoroughly understand the concepts of validity, contingency, and unsatisfiability as well as logical equivalence and entailment and consistency.

Once again this week, the Forum was a lively place. We were pleased to see so much discussion about the problems and the puzzles, with some people asking questions, some people providing answers, some people arguing that our answers are wrong (they are not), and others defending them.

This week, we finally get to logical reasoning - rules of inference, proofs, and so forth. We look at two different proof systems - the Mendelson proof system and the Fitch proof system. 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.

All of the exercises this week require that you do formal proofs, and many of you will find these exercises to be more challenging that the exercises in preceding weeks. Just remember, when you are doing a proof, first formulate a plan of how you are going to go about creating the proof. Often, this means starting at the end and thinking about how to derive the desired conclusion and then figuring out how to prove the intermediate results you need to prove the final result. If you are having trouble, look at the extras, and don't forget to stop by the discussion sessions on Tuesday and Thursday.

This week, we are releasing the videos and notes for Lesson 4. There is also a new puzzle. This one is relatively easy, but there are some really challenging ones coming.

mrg and Mikaela and Christina

By this point, you should have mastered the material in Lessons 1 and 2. From the Introduction, you should be familiar with the main topics of the course - logical languages, logical entailment and reasoning, formalization and automation. From Lesson 2, you should understand the syntax and semantics of Propositional Logic and the notions of evaluation and satisfaction. 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!

Judging by the discussion on the Forum, it appears that, for many of you, the toughest part of the first 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 want you to understand the distinction and relationship between sentences and the "worlds" that satisfy those sentences. (2) We want 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. It is like 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 who spent time answering these questions. Also those of you who shared your perspectives on open questions, puzzles, and so forth. 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 those of you who shared your logic puzzles and logic jokes.

This second week, your goal is to master the material in Lesson 3. You should understand the notions of validity and contingency and unsatisfiability, and you should understand the distinction between logical equivalence and logical entailment and logical consistency; and you should understand how to compute these properties for Propositional Logic.

This week, we are releasing the videos for Lesson 3. You already have the notes. (Chapter 3 under the Notes tab.) We are also releasing a new set of problems. There are some relevant Extras. Finally, for your edification and entertainment, there is a new puzzle - Logicians. You may also find it useful to look at some of the tools available under the Tools tab, notably Babbage (for generating simple truth tables) and Boole (for generating multicolumn truth tables).

Next week, we will see how to do proofs for Propositional Logic. In week 4, we will see a different approach to doing proofs. And stay tuned for upcoming special features - field trips and logic games, and a short somewhat irreverent piece on the making of the course.

Mike and Mikaela and Christina

PS: Click here for a logic cartoon / hint for this week's puzzle.

Okay. We are on our way! First week of class begins now. This week, your goal is to master the material in lessons 1 and 2.

The first lesson is easy enough. It is mostly overview. That said, you should not shortchange the material. The 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.

Lesson 2 is more substantive, but it is also easy. It introduces the syntax and semantics of Propositional Logic as well as the essentials concepts of evaluation and satisfaction. You should get comfortable with the language and you should get comfortable evaluating sentences and finding truth assignments that satisfy those sentences.

This week, you should also master the art of doing online problems. You should check out the Notes and the Extras and the Puzzles, and you should figure out how to use Discussion Forum.

A word about certificates. There are not approximately 70 problems in this course, and your grades on these problems will determine your overall grade for the course. We will be issuing certificates of accomplishment to all students who complete the course with a cumulative grade of 70% of the possible maximum score, and we will offer Statements of Distinction to all students who complete the course with a cumulative grade of 90% or more.

And a few words about the online problems. First of all, you can submit your answers to any problem as often as you like, and the system will take your highest grade. Second, all problems provide immediate feedback. When you check a checkbox or make a selection from a menu or compete a proof, the system will tell you immediately whether the answer is correct, even BEFORE you submit your answers for grading. The upshot is that, for some problems, there is no reason not to get a perfect score.

Yes, we realize that it is possible to "game" the system by dumbly trying all answers until you get the right one and then submitting that answer. However, this is already possible. There is nothing stopping you from signing up twice, getting the right answers from one account and using them in your other account. Besides, for many problems, mostly proofs, finding a correct answer is a challenge, and you will have to work hard to get that coveted green checkmark. And we do not reveal proofs until after the hard deadline.

The main reason for this seemingly lax approach to grading is our belief that there is great pedagogical value in immediate feedback rather than waiting for hours or days or even weeks to see the results. This is the first time doing things this way. When the course is over, let us know what you think.

You may notice that the notes and exercises differ a little from the videos and the graded problems (most noticeably in lessons 2 and 3). At the last minute, we decided to update the notes and revise the exercises, but we have not yet gotten around to updating the videos and graded problems. We highly recommend that you look at the notes and exercises there in addition to the videos and graded problems.

Finally, the administrators at Stanford would like to find out more about your background and motivation for taking this course. To this end, they have created a short pre-course survey for you. Please click here to take take the survey. Thank you.

mrg and Mikaela and Christina

We are happy to have you join us for this introductory course on Logic. This is the sixth time we are offering the course in this online format. We believe the online format has the potential for improving Logic education and for bringing the material to a wide audience.

The course consists of ten lessons on different aspects of Logic. Each lesson consists of several sections, each with its own video and notes and exercises. Our intent is to proceed through one or two lessons each week, which means you need to view a few hours of video and do a handful of exercises each week.

In addition to these lessons, the course contains some additional material, puzzles, and ancillary readings for those of you who want to explore beyond the primary material of the course. This additional 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 28. You should study the first lesson during the first week and do the corresponding problems within the following 9 days. If you miss the nominal deadline, you have an additional week to do the problems.

Importantly, you should take advantage of the discussion forum to communicate with your fellow students and with the instructors. Use the forum 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.

mrg and Christina and Mikaela