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Deductions is educational software designed to help students learn proofs in formal logic. It is intended to be used by instructors and students of college-level logic courses in philosophy, mathematics and computer science. It gives immediate feedback at each stage of a proof, provides hints about how to complete proofs, and comes with a set of video tutorials that explain and review several challenging concepts in logic.
Deductions aims to solve the three problems that make proofs the most difficult component of formal logic courses: not knowing whether rules are applied correctly, getting stuck in the middle of a proof, and uncertainty about the rules and strategies. Deductions addresses these issues by flagging errors, including a hint engine to make suggestions about how to complete a proof, and having multimedia tutorials to help students through complex rules.
1. Textbooks - Deductions is designed to work seamlessly with the following textbooks: (i) The Logic Book (by Bergmann, Moor, and Nelson), (ii) A Modern Formal Logic Primer (by Paul Teller), (iii) A Serious Introduction to Mathematical Logic (by Tony Roy). It also works with Modern Logic (by Graeme Forbes) with some adjustment, and because Deductions is highly configurable, it can work with other textbooks as well.
2. Flagging Errors - Deductions flags errors in proofs as soon as they occur. This is important, because when students are first learning proofs, Deductions prevents students from learning the wrong rules.
3. Hint Engine - Deductions provides hints about how to complete proofs. When students get stuck in the middle of a proof, Deductions suggests how to make progress.
4. Multimedia Tutorials - Deductions comes with a set of multimedia tutorials, divided into two groups: how to use Deductions to learn logic, and how to use the logic rules.
5. Flexibility - Deductions is designed to work with many different logic systems and textbooks. Both standard and alternative symbols are included, as well as rules that may be turned on and off individually.
6. Modern Design - Deductions provides a modern interface. As a new entry into a field that has not seen many updates in recent years (many logic programs are written for DOS, Windows 9x, or are rudimentary Java applets), Deductions leverages the technologies of Mac OS X to provide a clean user interface, drag-and-drop support, and a comprehensive help system.
7. More Efficient than Paper - Deductions takes care of the editing details. When working on paper, especially in large proofs, proofs must be reworked to add or remove lines, existing justifications must be renumbered, and so on. Deductions takes care of these housekeeping tasks by automatically adjusting proofs when lines are added, removed or moved.
System Requirements: Mac OS X 10.5 Leopard or Mac OS X 10.6 Snow Leopard
MacZot: What’s the most unique, useful feature of Deductions?
Wandering Mango: I’d have to say the most useful feature is different from the most unique feature. The most useful feature is that Deductions gives you immediate feedback on proofs; it lets you know whether you made a mistake right away. The most unique feature is the hint engine. Often, when you’re working on proofs in logic, you can get stuck. The hint engine gives you an idea how you might solve the problem.
MZ: Why did you create Deductions?
WM: I created Deductions because I have always been fascinated by computational logic, and because the vast majority of natural deduction apps lack a modern look and feel. When you look at the other natural deduction programs that are on the market, most of them are antiquated. They are written for DOS, or Windows 95. Some are rudimentary Java applets. As you might expect, these programs tend to be awkward and primitive. I wrote Deduction to have an intuitive user interface, and to be a modern alternative.
MZ: What is most interesting to you about developing software for the Mac platform?
WM: What is most interesting to me is the attention to design. From the Cocoa framework, to separation of the view and model, to the polished user interface that users expect, the Mac development environment is something really special. I’ve worked on other platforms, and so I really feel like I’ve come to a place where people are very interested in what your program does and how your program does it. It is the interest in “how” that sets the platform apart.
MZ: What features should a prospective buyer look into during a trial of your product?
WM: A prospective buyer should have a look at the video tutorials, and then if you know anything about natural deduction, run through some deductions to see how the program helps you learn. Deductions is a great tool, and this will give you a good idea how and why.
MZ: What are some interesting experiences you’ve had creating new versions of your software when OS is upgraded?
WM: An OS update always makes developers a little jittery, but so far everything has gone smoothly. I was able to plug directly into a number of Objective-C 2.0 features that came about it Leopard, and that made the development of Deductions a lot easier. I have no doubt that we’ll be incorporating some Snow Leopard technologies into Deductions too. I’m thinking about putting the hint engine into a separate thread using Grand Central Dispatch.
MZ: What features would you like to add to your product that at this time seem improbable/impossible?
WM: I’d really like to improve the hint engine to the point that it gives advice several steps ahead: not just “derive a contradiction,” but “derive this particular contradiction in order to achieve this particular goal.” Now for really fascinating reasons (to me, anyway) that have to do with the computability of predicate logic, there are fixed limits on just how far advice can go. But I’d love to do the research necessary to design a hint engine that presses right up against those fixed limits. That just seems out of reach right now.
MZ: What should a beginning logic student know before purchasing Deductions?
WM: If you are taking a class, you should know that formal logic is unlike mathematics in that the symbols and rules differ from textbook to textbook. Deductions works with several popular textbooks, and is very configurable, but it does not work with every textbook. If your textbook is The Logic Book by Bergmann, Moor and Nelson, A Modern Formal Logic Primer by Teller, or An Accessible Introduction to Serious Mathematical Logic by Roy, then Deductions will be of great help. If you are using some other textbook, Deductions may or may not be compatible; feel free to contact us if you’re not sure, or ask your instructor.
MZ: Can someone use Deductions even if not taking a logic course?
WM: Of course! Deductions has several video tutorials that you can follow, but if you really want to learn how to do proofs in formal logic, you’ll want to follow a textbook or set of lectures. Fortunately, Teller’s Modern Formal Logic Primer and Roy’s Accessible Introduction to Serious Mathematical Logic are freely available on the web.
MZ: What’s your favorite Mac app out there from another developer? Why?
WM: VoodooPad, without a doubt. I use it to keep track of notes, press releases, marketing, feature requests and business expenses. I use it to write the Deductions help files. I find it indispensable.
MZ: Can you us more about your company?
WM: I started Wandering Mango just this year, and Deductions is my first product. I’m hoping to make a go of it as a Mac indie developer. I think I’m lucky in that the market for Deductions is pretty well-defined (instructors and students who study formal logic in philosophy, mathematics, and computer science, and other people interested in formal logic).
MZ: What’s with the name?
WM: Well, Mac indie developers tend to have incongruous names that stick in your head: Rogue Amoeba, Flying Meat, Delicious Monster, and so on. Our name follows that tradition. A friend of mine decided that “Wandering Mango” sounded like a drink, and she created a recipe to celebrate our first app. It’s on our About page, and it’s really very tasty.