Logic lesson: A = {a, b}, Form = A+, Ax = {a}, R = {....

[tashe]

Hi everyone
I have a couple of lessons in my book that I just don't get. They seem so abstract to me. This is what its about. image.[attachment=0:2xfo3tgv]1.JPG[/attachment:2xfo3tgv]

Straight translation of the lesson name from my language to English would be
"Formal theories". I googled it, like i always do before bothering someone, but I can't find any example or a online book about it. Its horribly explained in the book and I dont see any chance to learn it from just reading the book. Exam is nearing and I'd be thankful to anyone that can point me to a book (free of course ) on the internet or some useful site or give me an insight to the problem.
Thanks

 

[stapel]

What is the meaning of "Form"? Is A a set containing the two elements "a" and "b"? What is A[sup:163o4b7w]+[/sup:163o4b7w]? What is Ax, and how does this set (?) relate to A?

What were the instructions? What are you supposed to do with these various items?

Please be complete. Thank you!

Eliz.

 

[tashe]

Re: Logic lesson

Sorry bout that. This is what's written in the textbook.
A is a alphabet containing the words {a,b}.
The Form is a language made from all the words from "a" and "b" plus the empty word. These are also called formulas and there is an algorithm which decides if a word is an element of Form.
Ax is a nonempty subset of Form. It's elements are called axioms.
R is a nonempty set of rules for making words.

And for the given example here is one answer. There are more probably.
bbba with a,ba,bba,bbba as proofs or b*b*b(this goes k-times)*a, for k>=0.
Help anyone?
Thanks

 

[stapel]

So this is definitely not a math question.... :shock:

I'm afraid that, in order to have any hope of understanding the (still unstated) question or the (stated) "givens", we almost certainly would need access to your text and/or your class notes. There are so many undefined or poorly-defined terms and relations that there seems no way to proceed.

Please provide all of the necessary background information. For instance, what are all of the axioms you have been given to use? What theorems do you have? How is a "form" formally defined? How is an "alphabet" formally defined? What is the definition of and rules for a "language"? How do axioms, being rules, relate to a language, being sets of "words" (and yet the axioms are somehow elements of subsets of the language, so rules are also words)?

If it is not possible to provide all of the necessary information (and I have a feeling that it isn't, short of typing out your textbook), you will need to consult with your instructor, work together with fellow students, or try a logic forum where the tutors are already familiar with your particular logical framework and definition set.

Eliz.