Stanford University
Philosophy
Reproduced with permission from NeXT Computer, Inc.
A Reference Guide to NeXT in Higher Education, Fall 1992
ยช 1992 NeXT Computer, Inc
Tarski's World supports leaning of first-order logic
first-order logic-the symbolic language at the core of modern logic-has become a requisite tool for studying a variety of disciplines, including philosophy, computer science, linguistics, and mathematics. In teaching first-order logic to students, Stanford University Associate Professor of Philosophy and Symbolic Systems John Etchemendy invariably encountered two problems.
"One," he says, "had to do with getting students to understand the central semantical ideas of first-order logic. The way these ideas are usually presented in textbooks makes them so abstract that students have a hard time understanding the point."
The other problem involved devising an efficient method for helping students who are having trouble expressing themselves in the first-order language. "That kind of help is difficult to give," says Etchemendy. "For example, when you give translation exercises, there is no single right answer: anything logically equivalent to a right answer is also a right answer. So someone has to read the answers carefully and try to see if they are logically equivalent to the right answer-an undecidable question, of course."
Although several computer-based tutorials on first-order logic were available to supplement class work, most focused primarily on syntactic concepts while, according to Etchemendy, "The main lesson of the last 50 years of research in logic has been that semantics are by far the most fundamental concepts to consider."
To help students master the semantic side of logic, Etchemendy and Indiana University Professor of Mathematics Jon Barwise developed a computer-based application called Tarski's World, named after a pioneer in the semantic approach to logic, Alfred Tarski. "Tarski's World makes the learning of the basic ideas of first-order logic more interesting, fun, and efficient than any other method we've found," says Etchemendy. "The application helps make the concepts concrete and understandable for students."
Etchemendy and Barwise developed the application on Macintosh, MS-DOS, and NeXT platforms, but Etchemendy says, "The NeXT version was much easier to develop than the other two. With Interface Builder and all the other development apps in the NeXTSTEP environment, developing with NeXTSTEP was a dream come true-it took our NeXT programmer, Eric Ly, no time to create the application. We worked more effciently than we could have on any other machine. NeXT is just wonderful compared to the Macintosh-and the Mac is great compared to Windows. The app took
forever to finish on Windows.
"I also think that students can work more efficiently on the NeXT," he adds. "Because of the machine's large monitor and multitasking environment, students are able to work with multiple windows of the application at the same time."
In Tarski's World, students build three-dimensional worlds inhabited by various geometric figures and then test sentences of first-order logic to determine whether they are true or false in these worlds. In one exercise, for example, students are given a series of sentences and asked to build a single world in which all the sentences given are true. Students are also assigned exercises on multiple quantifiers and their interaction with negation.
One of the main features of Tarski's World is its use of games to help students understand the concepts of first-order logic. Students might be asked, for example, to evaluate sentences in a constructed world. If their evaluations are incorrect, the applications provides them with a game that helps them understand where they went wrong.
"Tarski's World opens up many ways to teach what first-order sentences mean," says Etchemendy. "With Tarski's World, we're not limited to the abstract task of translating back and forth from English: we can directly describe worlds, use the language to identify objects and construct worlds satisfying a description."
In his introductory courses, Etchemendy uses exercises from Tarski's World in the classroom as well as for homework assignments. He frequently assigns additional exercises to students in the course who are having a difficult time with the first-order language. He also uses Tarski's World in his advanced logic courses to assist students who have yet to master first-order logic.
"Rather than let these students flounder, we wanted a tool that we could simply hand them and let them work through on their own. Tarski's World serves this function remarkably well."
For more information, please contact:
John Etchemendy
Associate Professor of Philosophy and Symbolic Systems
Center for the Study of Language and Information
Stanford University
STANFORD, CA 94305-4115
(415) 725-2315
etch@russell.stanford.edutholland@pars.skidmore.edu