HELP translating arguments into PREDICATE logic? Truth tables?
Greetings,
I am have difficulty translating my argument into Prepositional logic. Please help me. Here is my argument
Premises:
Net neutrality limits the number and type of perspectives accessible and relegates all competitors to the fringe. Granted, there have always been alternatives to mainstream media, such as underground 'zine culture and public access television. However, it wasn't until Google's PageRank and desktop publishing came along that such channels could be organized by merit and given an equal voice. Pushing Internet providers into the content business is destructive to all involved. Users are limited to the content approved by their provider, assuming they can afford it. Content providers and application developers are returned to the fringe, their success determined entirely by the earnings they present to the ISP.
Competition in the Internet service market is severely hampered, limited not by entry costs or management difficulties, but by a system of content partnerships and a conflation of interests. Most confusingly, limited options and higher costs will inevitably lead to lower usage and slowed growth, bad results for those in the business of facilitating Internet access. If “Carriers make money only by carrying more traffic” it's confusing that they would seek to limit their customers' ability to use their product (Thierer 3). The legal decisions to label Internet service providers as information services enables a constriction of choice, at every level of this complex system, that defies the nature of the network and will recreate the shortcomings of centralized, restrictive media channels.
Conclusions:
We can conclude that that companies should be allowed to do whatever they wish to do with their own networks. This is not a fair and justified argument since internet providers do not have the right to discriminate between the amount of data which is accessible to the user and which is not. The basics of the Internet were laid down to share anything the user wishes to share. In the same fashion telephone networks don’t have the right to discriminate to decide whom you can call. Internet should be free and ISP should not predefine what sites should be accessible to the users.
Answers & Comments
Verified answer
When doing proofs, the number of possible cases can sometimes explode dramaticly. Unfortunately programs dealing with this often follow suit.
THEREFORE: I have made a number of simplifying assumptions which help to cut down on the problem. (Hopefully none of them will cause me any problems later.)
Unique lines
A given result may appear ONLY ONCE in the currently active (Non-discharged) proof. Any reference to the second one could be mapped to a reference to the first one without loss of generality or complication.
Connonical forms
When theorems are looked up, they are first reduced to a connonical form. This form differs from the original only in renaming of variables. This allows a fast [hashed] lookup to be done, instead of having to search through all the stored theorems.
Internal form
The storage form of an expression is LISP style notation such as:
(IMP (IMP p q) (EXISTS x (IMP p q)))
This form is converted into trees inside the program and most routines walk those trees.
Program Flow
The program first gives a welcome screen, and requires the user to select a notational system. This enables the user to see the later steps (such as selecting an axiom system) in the notation of her choice.
The program then gives the user a chance to select an Axiom System to use as a basis for the proof.
The program then allows the user to state a proof goal. This is optional, but if the goal is stated the program may be able to provide some suggestions later.
Currently no natural deduction proofs can be done. (Code to handle assumptions and discharges not functional yet.)
Each step that can be taken at a given point has a Button or Link that takes that step.
An example output derivation is: (CS notation, default system)
1: p>(q>p) Axiom A1
2: (p>(q>r))>((p>q)>(p>r)) Axiom A2
3: p*q>p Axiom A3
4: p*q>q Axiom A4
5: p>(q>p*q) Axiom A5
6: p>p+q Axiom A6
7: q>p+q Axiom A7
8: (p>r)>((q>r)>(p+q>r)) Axiom A8
9: (p==q)>(p>q) Axiom A9
10: (p==q)>(q>p) Axiom A10
11: (p>q)>((q>p)>(p==q)) Axiom A11
12: (-p>-q)>(q>p) Axiom A12
Stated Goal: (p*q>p)*(p*q>q)
13: (p*q>p)>((p*q>q)>(p*q>p)*(p*q>q)) 5,US,p*q>p/p, p*q>q/q
14: (p*q>q)>(p*q>p)*(p*q>q) 3,13,MP
15: (p*q>p)*(p*q>q) 4,14,MP
Futures
I'm accepting suggestions for alternate notations and systems.
Now that quantifiers are in both the I/O routines and in substitution, there need to be rules that use quantifiers. User interface issues are the main problem.
I need to rewrite the initialization code so that systems can be put together by gathering menu choices instead of requiring that the entire system be read in at once. That would allow having alternate PC basies for each modal logic system.
The parse trees that are drawn by the debugging code need to be made availiable as an output alternative. They are much too well liked.
I need to write an I/O module that understands dots (as Russell and Whitehead used) as in a>.b>c=..a>b>c.
One really ought to be able to change output notation in the middle of a proof. (So, for example, you can convert to a "pretty printed output" notation for printing without having to deal with it for the proof.)
The "Known Theorem" tables need to have some substatial lists added, instead of the current stubby 4.
When the proof is done, I need to have some cleanup commands.
The canned proof tables need some useful examples.
Much of the code needs to be split out as separate modules so that the other tools can make use of it.
Assumption and discharge display code needs to be added. (Argh... yet more work on the restrictions of the substition code.)
Should the internal form of the derivation be made availiable (I.E. should you be able to import and export them?)? They look roughly like: Example Derivation But the format is prone to change.
Should Substitution be a simple button, with the substitutions boxes themselves only displayed when you say you want to do one? It would make the output look dramaticly cleaner, but would mean it takes two screens to do a substitution.
Should axioms be dragged into the proof only as needed? (I think that they still need to be fully listed, but the proofs are shorter if only the axioms used appear in the final proof.)
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