Re: Exotic Logics
On Jun 17, 10:32 am, Aaron Brady castiro...@gmail.com wrote: On Jun 17, 10:23 am, Mensanator mensana...@aol.com wrote: snip I think high and low /voltages/, though continuous and approximate, might satisfy this. There are no such things as electrons, I've got a Tesla coil if you'd like to meet some electrons personally. The Wall Street Journal ran an article about Asian pleasure markets; they provide a-- quote-- perfectly reasonable professional option. For shame, Lieutenant. Always cite your source. http://online.wsj.com/article/SB124416693109987685.html Last paragraph, second to last sentence. It was a book review of _The East, the West, and Sex_ by Richard Bernstein . -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
William Clifford wrote: I've read one can do all of the 16 binary operations with clever uses of NAND or NOR. That is correct. In fact semiconductor logic is done using these two principle gates. See http://en.wikipedia.org/wiki/NAND_logic . Quite interesting really. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
Michael Torrie wrote: William Clifford wrote: I've read one can do all of the 16 binary operations with clever uses of NAND or NOR. That is correct. In fact semiconductor logic is done using these two principle gates. See http://en.wikipedia.org/wiki/NAND_logic . Quite interesting really. Not is done but could be done. As your reference correctly points out, However, contrary to popular belief, modern integrated circuits http://en.wikipedia.org/wiki/Integrated_circuit are not constructed exclusively from a single type of gate -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? First question: what's an exotic logics? Do you mean things like three-value logic, fuzzy logic, probabilistic reasoning, etc? Or do you mean logical operators others than and, or, xor, nand, nor, etc? Or both? Something else? I did some searching but not being too sure of what to look for and carried away with my own enthusiasm for the idea, I didn't find much. What I've come up with is, no doubt, inefficient, naive, poor python style, and probably wrong in fundamental ways too subtle for me, but here it is: import itertools import operator class Logic(): class of generic logic operators [...] If (nearly) all your methods are static methods, chances are a class is the wrong solution. Why not just define the static methods as top-level functions? This seemed to be working for the limited tests I did on it, while I was doing them. The following checked out last time I tried: and_ = Logic(2, 8) or_ = Logic(2, 14) xor = Logic(2, 6) I have no idea how to validate the results of the trinary and beyond logics. The same way you would validate and_, or_ and xor: to validate something, you need to know what the correct answer is, then compare the answer you get with the answer you should get. For a binary operator and binary operands, you can exhaustively check every valid input: flag1 op flag2 there are four combinations of input flags: 0 op 0 0 op 1 1 op 0 1 op 1 For three-valued logic, there are 9 combinations. For four-valued, 16. So exhaustively testing all the possible inputs is quite simple. As far as getting the correct answers, you have to decide which three- valued logic(s) you want to use, then go look them up. Or just make them up yourself! E.g. given trinary flags 0, 1, 2, (say), you might want the operators to give the same results with 0, 1 as they would if you were applying it to binary flags 0, 1. E.g.: # binary operands 0 and 0 = 0 0 and 1 = 0 1 and 0 = 0 1 and 1 = 1 # trinary operands 0 and 0 = 0 0 and 1 = 0 0 and 2 = ? # probably 0 1 and 0 = 0 1 and 1 = 1 1 and 2 = ? # could be 0, or maybe 1 2 and 0 = ? # probably 0 2 and 1 = ? # 0 or 1 2 and 2 = ? # probably 2 Different choices lead to different versions of ternary logic. Thanks for reading and trying this out. Corrections? Criticism? Comments? You're implementation seems rather confusing. I think that's partly because you use lots of abbreviated jargon terms that mean little or nothing to me: rdx, opr (operator?), lsd, pute. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? def true(x, y): return x def false(x, y): return y def print_bool(b): print b(true, false) print_bool(true) print_bool(false) def Not(b): def not_b(x, y): return b(y, x) return not_b print_bool(Not(true)) print_bool(Not(false)) print_bool(Not(Not(true))) def And(a, b): return a(b, a) def Or(a, b): return a(a, b) print_bool(And(true, true)) print_bool(And(true, false)) print_bool(Or(false, true)) print_bool(Or(false, false)) -- Steven -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
Steven D'Aprano wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? def true(x, y): return x def false(x, y): return y def print_bool(b): print b(true, false) String isn't considered object? Also, b/true()/false() is a function object, isn't it? Unless function is first-class, you can't pass them around like that, since you need a function pointer (a.k.a number); but if function is first-class then there it is an object. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 1:44 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? snip I think high and low /voltages/, though continuous and approximate, might satisfy this. There are no such things as electrons, only variations in density of the luminiferous ether. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 1:28 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? First question: what's an exotic logics? Do you mean things like three-value logic, fuzzy logic, probabilistic reasoning, etc? You (OP) may be interested in the definitions of the fuzzy operators: and( x, y ) := min( x, y ) or( x, y ) := max( x, y ) not( x ) := 1 (one)- x nand( x, y ) := not( and( x, y ) ) = 1- min( x, y ) Defining 'xor' as '( x or y ) and ( not( x and y ) )', we have: xor( x, y ) := min( max( x, y ), 1- min( x, y ) ) However, defining 'xor' as '( x and not y ) or ( y and not x )', we don't have: xor( x, y ) := max( min( x, 1- y ), min( y, 1-x ) ) Good question. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 5:37 pm, Lie Ryan lie.1...@gmail.com wrote: Steven D'Aprano wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? def true(x, y): return x def false(x, y): return y def print_bool(b): print b(true, false) String isn't considered object? Also, b/true()/false() is a function object, isn't it? Unless function is first-class, you can't pass them around like that, since you need a function pointer (a.k.a number); but if function is first-class then there it is an object. What Steven was doing was implementing some of the more basic stuff from Lambda calculus in python. If you're implementing a different system in an existing language, you'll need to use _some_ facilities of the original language to interface with the outside world. Anyway, here's a sample interactive session I just tried: def a(stuff): ... print stuff ... def b(stuff): ... stuff(abc) ... b(a) abc functions are first-class citizens in python. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 10:04 am, Aaron Brady castiro...@gmail.com wrote: snip You (OP) may be interested in the definitions of the fuzzy operators: and( x, y ) := min( x, y ) or( x, y ) := max( x, y ) not( x ) := 1 (one)- x nand( x, y ) := not( and( x, y ) ) = 1- min( x, y ) Defining 'xor' as '( x or y ) and ( not( x and y ) )', we have: xor( x, y ) := min( max( x, y ), 1- min( x, y ) ) However, defining 'xor' as '( x and not y ) or ( y and not x )', we don't have: xor( x, y ) := max( min( x, 1- y ), min( y, 1-x ) ) Corollary: xor1( x, y ) === xor2( x, y ). Non-exhaustive demonstration, excerpt: def xor1( x, y ): ... return min( max( x, y ), 1- min( x, y ) ) ... def xor2( x, y ): ... return max( min( x, 1- y ), min( y, 1- x ) ) ... for i in range( 0, 11, 2 ): ... for j in range( 0, 11, 2 ): ... print i, j, xor2( x, y )*10, ' ', ... print 0 0 0.00 2 2.00 4 4.00 6 6.00 8 8.0 2 0 2.02 2 2.02 4 4.02 6 6.02 8 8.0 4 0 4.04 2 4.04 4 4.04 6 6.04 8 6.0 6 0 6.06 2 6.06 4 6.06 6 4.06 8 4.0 8 0 8.08 2 8.08 4 6.08 6 4.08 8 2.0 10 0 10.0 10 2 8.0 10 4 6.0 10 6 4.0 10 8 2.0 They appear to be equal. I forgot to mention, fuzzy values take on values from the continuous open or closed range 0 to 1. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 11:59 am, Aaron Brady castiro...@gmail.com wrote: On Jun 17, 1:44 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? snip I think high and low /voltages/, though continuous and approximate, might satisfy this. There are no such things as electrons, I've got a Tesla coil if you'd like to meet some electrons personally. only variations in density of the luminiferous ether. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 10:05 am, pdpi pdpinhe...@gmail.com wrote: On Jun 17, 5:37 pm, Lie Ryan lie.1...@gmail.com wrote: Steven D'Aprano wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? def true(x, y): return x def false(x, y): return y def print_bool(b): print b(true, false) String isn't considered object? Also, b/true()/false() is a function object, isn't it? Unless function is first-class, you can't pass them around like that, since you need a function pointer (a.k.a number); but if function is first-class then there it is an object. What Steven was doing was implementing some of the more basic stuff from Lambda calculus in python. If you're implementing a different system in an existing language, you'll need to use _some_ facilities of the original language to interface with the outside world. Sir! Entropy levels are approaching dangerously low levels. We don't even have enough entropy to fi -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 10:23 am, Mensanator mensana...@aol.com wrote: On Jun 17, 11:59 am, Aaron Brady castiro...@gmail.com wrote: On Jun 17, 1:44 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? snip I think high and low /voltages/, though continuous and approximate, might satisfy this. There are no such things as electrons, I've got a Tesla coil if you'd like to meet some electrons personally. The Wall Street Journal ran an article about Asian pleasure markets; they provide a-- quote-- perfectly reasonable professional option. -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Jun 17, 1:28 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? First question: what's an exotic logics? Do you mean things like three-value logic, fuzzy logic, probabilistic reasoning, etc? Or do you mean logical operators others than and, or, xor, nand, nor, etc? Or both? Something else? The short answer is 'yes'. Obviously, I don't know much about this stuff. I was looking a table of different operators and their truth values and saw that these were just different ways of reading and comparing numbers. I wrote this code to explore this idea in a general sense and see where it leads and learn something about computers. [...] If (nearly) all your methods are static methods, chances are a class is the wrong solution. Why not just define the static methods as top-level functions? That is exactly how they started. I wrapped them up in an class because I thought I might want to create a bunch of them for testing and experimentation. I'm curious to see how combinations of functions give the same (or different) results. I've read one can do all of the 16 binary operations with clever uses of NAND or NOR. [SNIP] You're implementation seems rather confusing. I think that's partly because you use lots of abbreviated jargon terms that mean little or nothing to me: rdx, opr (operator?), lsd, pute. Sorry about the confusion. It's because I'm confused. I should check out a book on the subject. Thanks for your help. -- William Clifford -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
William Clifford wrote: same (or different) results. I've read one can do all of the 16 binary operations with clever uses of NAND or NOR. The book Laws of Form, by Spencer-Brown' is based on that observation, with nand/nor expanded to n-ary 'bag' functions (like sum() is). I recommend it, especially if you can find it in a library. tjr -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
pdpi wrote: On Jun 17, 5:37 pm, Lie Ryan lie.1...@gmail.com wrote: Steven D'Aprano wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? def true(x, y): return x def false(x, y): return y def print_bool(b): print b(true, false) String isn't considered object? Also, b/true()/false() is a function object, isn't it? Unless function is first-class, you can't pass them around like that, since you need a function pointer (a.k.a number); but if function is first-class then there it is an object. What Steven was doing was implementing some of the more basic stuff from Lambda calculus in python. If you're implementing a different system in an existing language, you'll need to use _some_ facilities of the original language to interface with the outside world. Anyway, here's a sample interactive session I just tried: def a(stuff): print stuff def b(stuff): stuff(abc) b(a) abc functions are first-class citizens in python. I've just reread my sentence, and even I wouldn't have understood (or would misunderstood) what I was talking about if it was worded like that. What I meant was: if you can pass a function as an argument to another function, that means either: 1) you must use function pointer (numbers) or 2) function is a first-class object. Both violates the restriction (no number and no object respectively). Even after abandoning the semantics of functions in python, going to function as in purely mathematical sense, I still am not convinced (warning: I don't know lambda calculus, although I program in heavily functional style). PS: the string comment was meant to be a joke... -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
Quoting Lie Ryan lie.1...@gmail.com: pdpi wrote: On Jun 17, 5:37 pm, Lie Ryan lie.1...@gmail.com wrote: Steven D'Aprano wrote: On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote: I was staring at a logic table the other day, and I asked myself, what if one wanted to play with exotic logics; how might one do it? This might be useful for you, and if not useful, at least it might blow your mind like it did mine. (This is not original to me -- I didn't create it. However, I can't find the original source.) Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? [basic lambda calculus definitions] [...] What I meant was: if you can pass a function as an argument to another function, that means either: 1) you must use function pointer (numbers) or 2) function is a first-class object. Both violates the restriction (no number and no object respectively). Even after abandoning the semantics of functions in python, going to function as in purely mathematical sense, I still am not convinced (warning: I don't know lambda calculus, although I program in heavily functional style). You are confusing semantics with implementation. At some point, of course one would need to use real object (at the lowest level, the computer I'm typing this in is a physical object). But the interesting part is that you can define the whole logic system using nothing but functions. You may need to implement it using objects, or maybe you could devise a machine that will behave like that using only sticks on the floor, but that doesn't matter. From the user's perspective, there would be only functions: no strings, no objects, no numbers. That reminds me of my last class (disclaimer: I teach discrete math). I told my students well, let's assume that numbers exist, and I wasn't making fun of them... I found that topic easier to understand (computability, primitive recursion) if one ignores the numbers, even if one obviously has to write them somewhere at some point. -- Luis Zarrabeitia Facultad de Matemática y Computación, UH http://profesores.matcom.uh.cu/~kyrie -- Participe en Universidad 2010, del 8 al 12 de febrero de 2010 La Habana, Cuba http://www.universidad2010.cu -- http://mail.python.org/mailman/listinfo/python-list
Re: Exotic Logics
On Wed, 17 Jun 2009 16:37:04 +, Lie Ryan wrote: Imagine for a moment that there are no boolean values. There are no numbers. They were never invented. There are no classes. There are no objects. There are only functions. Could you define functions that act like boolean values? And could you define other functions to operate on them? ... String isn't considered object? handwave/ Given that the strings only exist inside one function specifically for printing, I think we can ignore that. If you prefer, print_bool() could look at the function names, that would work just as well. One way or the other, we have to get human-readable names into the system *somehow*. Also, b/true()/false() is a function object, isn't it? Unless function is first-class, you can't pass them around like that, since you need a function pointer (a.k.a number); but if function is first-class then there it is an object. That's an implementation detail. So long as you can pass around functions, and return them, then it doesn't matter whether they are implemented as objects or not. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
