[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 590: sizeof(): Parameter must be an array or an object that implements Countable
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 646: sizeof(): Parameter must be an array or an object that implements Countable
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 472: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 113: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
Logical rules and inferences - Toki Pona Forums

Logical rules and inferences

Mind and thought: Wisdom, mental health, cognition, self-talk, consciousness, philosophy, psychology, optimizing your thinking, productivity hacks
Menso kaj penso: Saĝaĵoj, psiĥa sano, kogno, memparolado, psiĥa stato, filozofio, psikologio, rearanĝi sian pensadon, plibonigi sian produktokapablon
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable
jan_Niko
Posts: 8
Joined: Wed Oct 21, 2009 9:40 am
Location: ma Epelanto
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Logical rules and inferences

Postby jan_Niko » Wed May 05, 2010 11:03 am

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
Posts: 1545
Joined: Wed Dec 02, 2009 12:21 pm
Location: Takoma Park, MD
Contact:

Re: Logical rules and inferences

Postby janMato » Wed May 05, 2010 5:34 pm

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
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Logical rules and inferences

Postby janKipo » Thu May 13, 2010 5:55 pm

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
Posts: 8
Joined: Wed Oct 21, 2009 9:40 am
Location: ma Epelanto
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Logical rules and inferences

Postby jan_Niko » Fri May 14, 2010 4:03 pm


janKipo
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Logical rules and inferences

Postby janKipo » Fri May 14, 2010 5:51 pm

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
Posts: 8
Joined: Wed Oct 21, 2009 9:40 am
Location: ma Epelanto
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Logical rules and inferences

Postby jan_Niko » Fri May 14, 2010 8:43 pm

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
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Logical rules and inferences

Postby janKipo » Fri May 14, 2010 10:43 pm

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).


[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Return to “sona pona”

Who is online

Users browsing this forum: No registered users and 3 guests

cron