Logical rules and inferences

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jan_Niko
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Logical rules and inferences

Post by jan_Niko »

I have been thinking about how to translate rules and inferences in symbolic logic into toki pona. Here are a few of my ideas. Criticisms and corrections are welcome. There are many things that I left out (biconditionals, for example) because I couldn't come up with a good way to express them.

Rules of inference

Modus Ponens:
p ⊃ q, p / ∴ q
nasin pi Motusi Poneni
ijo li lon la ijo ante li lon.
ijo li lon.
ijo ante li lon.

Modus Tollens:
p ⊃ q, ~q / ∴~p
nasin pi Motusi Toleni
ijo li lon la ijo ante li lon.
ijo ante li lon ala.
ijo li lon ala.

Disjunctive Syllogism:
p v q, ~q / ∴ p
ijo anu ijo ante li lon.
ijo ante li lon ala.
ijo li lon.

Conjunction:
p, q / ∴p ∙ q
ijo li lon.
ijo ante li lon.
ijo en ijo ante li lon.

Addition:
p / ∴ p v q
ijo li lon.
ijo anu ijo ante li lon.

Simplification:
p ∙ q / ∴ p
ijo en ijo ante li lon.
ijo li lon.

Replacement rules

Double Negation:
~~p :: p
ijo li lon ala ala.
ijo li lon.

Contraposition:
p ⊃ q :: ~q ⊃ ~p
ijo li lon la ijo ante li lon.
ijo ante li lon ala la ijo li lon ala.

De Morgen's:
~(p v q) :: ~p ∙ ~q
ni li ala: ijo anu ijo ante li lon.
ijo en ijo ante li lon ala.

Duplication:
p :: p v p (OR p :: p ∙ p)
ijo li lon.
ijo anu ijo sama li lon. (OR ijo en ijo sama li lon.)
janMato
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Re: Logical rules and inferences

Post by janMato »

Looks good as any proposal. Personally, I prefer to have the verbal reading of a foreign language (mathematical notation), pay no or little attention the grammar of the mathematicians natural language (or favorite conlang)

a^2 + b^2 = c^2 --> a squared plus b squared equals c squared. This is (nearly) only the string of characters being read by name as they appear.

*not* "So someone today squares this "a" and they combine it with a b, which is also squared and that all together equals this c times itself."
janKipo
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Re: Logical rules and inferences

Post by janKipo »

Well (sorry, I but I did this stuff for a living for 43 years), the inferences are in the object language but the tp versions are in the metalanguage (e.g., talks about truth and the like). Also note that modus ponens is strictly modus ponendo ponens and MT modus tollendo tollens, so that disjunctive syllogism can be called modus tollendo ponens (the missing modus ponendo tollens is ~(P & Q), P :. ~Q). This presentation looks a lot like the later Aristotelian (misre)presentation of Stoic logic, but I don't see the point of it for tp.
jan_Niko
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Location: ma Epelanto

Re: Logical rules and inferences

Post by jan_Niko »

janKipo wrote:This presentation looks a lot like the later Aristotelian (misre)presentation of Stoic logic
Really? I trust you since you did this for a living, but I'm surprised because it's what is presented in my symbolic logic textbook.
janKipo wrote:I don't see the point of it for tp.
For fun.
janKipo
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Joined: Fri Oct 09, 2009 2:20 pm

Re: Logical rules and inferences

Post by janKipo »

Good Lord! Is Copi still around? (Another book that was notorious for getting levels mixed up). The point is that these inferences are from sentences to sentence, not from claims about certain sentences being true to others being true. "Its either a sheep or a goat. It's not a goat. So it is a sheep" is Disjunctive Syllogism (MTP); "It is true that it is either a sheep or a goat. It is false that it is a goat. Therefore it is true that it is a sheep." is not (since, inter alia, it contains neither a disjunction nor a negation).
jan_Niko
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Location: ma Epelanto

Re: Logical rules and inferences

Post by jan_Niko »

Sorry that this no longer has anything to do with Toki Pona, but...

I used Understanding Symbolic Logic (5th Edition) by Virginia Klenk. Do you have any recommendations for better books?
janKipo
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Joined: Fri Oct 09, 2009 2:20 pm

Re: Logical rules and inferences

Post by janKipo »

Gee, I think I reviewed the first edition of that lebbenty lebben years ago. I don't remember anything about it, but, if it said something like what Mato seems to be saying, I sure would have objected strongly. Since it has gone through five edition in a world where there are a lot of competitors, it must be at least decent (Copi went through a dozen or so when there were first no serious competitors and then so many people trained on Copi that kept using it out of habit). I'll have took at what she actually says to see if there may be some misinterpretation involved here. The book I started out with was really terrible -- in all the ways I have hinted at -- but it got me hooked and I went on to better ones (after struggling through Principia Mathematica for a stretch). My own books (which were rather quirky and nonstandard in a variety of ways) have been op since the 1980s and never circulated far from St. Louis (one of my students used one in N.Carolina once, I think) . Them aside, the best book I remember using was Kalish and Montague (and Mar in later editions) but I came to that after I was already a decent logician, so it may not be so simple (though I did teach intro from it for several years without any unusual problems). The other one, which was even easier to teach from, was Anderson and Johnson's Natural Deduction, but that disappeared after I had used it for a couple of years and never came back (part of the reason I wrote my own). I haven't kept up with anything in the last 10 years, so I don't know what all is out there, though I assume (or hope) that some good stuff is available, hopefully with good heuristic programs along side (I never got my programs running, another reason why they are all op -- aside from their being crappy).
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