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The Game of Modern Logic By Layman E. Allen Professor of Law and Senior Research Scientist, University of Michigan |
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The Game of Modern Logic By Layman E. Allen Professor of Law and Senior Research Scientist, University of Michigan |
Adventurous WFF 'N PROOF Strategies
Strategies of Constructing PROOFs and Strategies of Play *
1. Strategies of Constructing PROOFs
A. Grand Strategy
Try first to prove it directly;
if that fails, try to prove it indirectly.
| Example 1A1. | To prove: NKNpq --** ApNq |
| . | NKoAi: NKNpq --** ApNq
1|_NKNpq s 2|a|_q s (Trying to prove Nq at 1st level, |b|1|_p s and then ApNq, by Ai) | |2| : | |3| q aR | |4| Np ? (Fails at this step, as all other | |5| KNpq 4,3,Ki direct efforts will somehow fail) | |6| NKNpq 1RR |c| Np b,Ni |d| KNpq c,a,Ki |e| NKNpq 1R 3| Nq 2,Ni 4| ApNq 3,Ai |
Failed trying to prove it
directly; so try proving it indirectly.
In mathematical logic the
No Rule is called the Rule of Indirect Proof; the Ni Rule is called Reductio
ad Absurdum.
So, try No.
| NKoAi: NKNpq --** ApNq
1|_NKNpq s 2|a|_NApNq s |b|1|_Np s | |2|a|_q s | | |b| KNpq 1R,a,Ki | | |c| NKNpq 1RRR | |3| Nq 2,Ni | |4| ApNq 3,Ai | |5| NApNq aR |c| p b,No |d| ApNq c,Ai |e| NApNq a,Rp 3| ApNq 2,No |
B. C2A Conversion
Where the 18 Basic Derived Rules are available for
purposes of constructing proofs (in PC Proof -- Game 20 and
Frantic WFF 'N PROOF -- Game 21), use C2A Conversion
(the CoAi Rule) to transform the objective from getting to
an A-WFF to getting to a C-WFF, and then getting
to the A-WFF from the C-WFF by the CoAi Rule.
| Example 1B1. | To prove: NKNpq --** ApNq |
| . | NKoAi: NKNpq --** ApNq
1|_NKNpq s 2|a|_Np s |b)1|_q s | |2| KNpq aR,1,Ki | |3| NKNpq 1RR |c| Nq b,Ni 3| CNpNq 2,Ci 4| ApNq 3,CoAi |
2. Strategies of Play -- The Devastating Duo: SSU and BAF
| Here, there is a available a powerful Learning Program to gain mastery of these two strategies that every serious player of Adventurous WFF 'N PROOF should work through completely. |
Example 2A1.
Given the Resources: CRR pps ...
to set the Goal: Csp
is a SSU, because by doing so you have snuggled up to within one move of
being an A-Flub. Either
1) transferring the remaining p to Permitted Premisses or Essential,
or
2) transferring a remaining R to Permitted Rules or Essential,
on the next move will be an A-Flub.
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| Csp | p/R(P2a1) | P2A1: p --** Csp
1|_p s 2|a|_s s |b| p 1R 3| Csp 2,Ci |
Example 2A2.
Given the remaining Resources: AKNNNRR prqss ...
with the Goal: KpANrNq
and the already allocated Resources: Permitted Premisses:s Permitted Rules:
Essential:
to move an s to Essential is a DSU, because by doing so you have
snuggled up to within one
move of being an A-Flub. Either
1) transferring a remaining N to Permitted Premisses or Essential,
or
2) transferring a remaining R to Permitted Rules or Essential,
on the next move will be an A-Flub.
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| KpANrNq | s,Ns/R(PR2A2) | PR2A2: s,Ns --** KpANrNq
1| s s 2|_Ns s 3|a|_NKpANrNq s |b| s 1R |c| Ns 2R 4| KpANrNq 3,No |
B. BAF (Bold A-Flub)
Example
2B1. Given the Resources: CCNNRR pps ...
to set the Goal: CNCppNs
may well be a BAF, because by doing so you have made an A-Flub.
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| CNCppNs | /R(PR2B1) | PR2B1: --** CNCppNs
1|a|_NCNCppNs s |b| KNCppNNs a,NCoKi |c| NCpp b,Ko |d| KpNp c,NCoKi |e| p d,Ko |f| Np d,Ko 2| CNCppNs 1,No |
Remember,
| Here, there is a available a powerful Learning Program to gain mastery of these two strategies that every serious player of Adventurous WFF 'N PROOF should work through completely. |
| If you notice any typographic errors or have any other
suggestions for improving this web page, please notify me at the email
address:
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