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From: "'John E Clifford' via lojban" <lojban@googlegroups.com>
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Subject: Re: [lojban] Lojban is a logical failure
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 Fascinating. =C2=A0But since it is totally locked in to the structure (or =
lack of it) of Lojban, it is ultimately uninteresting. =C2=A0The real quest=
ion is to figure out what the structure of Lojan should be, given the struc=
ture of Language. =C2=A0And, since that is not yet given, except very vague=
ly, that becomes the real question. =C2=A0I think that, if the language que=
stion is answered, the Lojban (or whatever it wil finally be called) questi=
on will fall into place quite directly (though not easily). =C2=A0But, sinc=
e no one in this group is working on the basic problem, I don=E2=80=99t see=
 the point of patching the leaky boat with more soluble paper.
    On Friday, April 2, 2021, 06:48:21 AM CDT, Corbin Simpson <mostawesomed=
ude@gmail.com> wrote: =20
=20
 Hi Mike,
While you're correct that the number of rules will not be ~10, like in a ty=
pical logic, but more like ~10,000; I do not find this to be a serious obst=
acle. Metamath [0] has tens of thousands of handwritten derivations, and a =
machine can check that they are well-formed and valid proofs in only a few =
seconds. I think that the main difficulty is in composing the rules in the =
first place.
The semantics I recommend for Lojban is a fragment of second-order logic (S=
OL). This embeds cleanly into HOL. Proof search is infeasible, but that is =
typical of programming languages; rather than hypernymy getting in the way =
of proof search, hypernymy offers many choices for folks writing in Lojban =
to express themselves with nuance.
There exist at least two gismu, {dugri} and {tenfa}, which address the same=
 underlying relation. As an immediate and very satisfying consequence, Lojb=
an cannot have a normal form without some arbitrary violence [6] to the bas=
eline, in the form of a choice which well-orders the gismu. (We could go al=
phabetically, of course.)

Many words have been spilled on tanru. To be brief, writing (=3D>) for impl=
ication, I recommend the principles that:
* Each lujvo =3D> each implied seljvajvo [1] from its terbri
* Each lujvo =3D> the tanru it was made from* Each tanru =3D> its tertau
So, for example, from {nanbymlatu} "catloaf; cat sitting in a loaf shape" w=
e could conclude {mlatu} "cat". Similarly, from {xekri mlatu} "black cat" w=
e could conclude {mlatu}. It is okay that adjectives are vague; they still =
constrain what's logically possible, and that is enough.
Note also that, borrowing a bit of category theory, we should expect some a=
llegory-like [7] behavior here. Specifically, if we imagine the (hypothetic=
al!) rule that {xekri} =3D> {skari}, then {xekri mlatu} =3D> {skari mlatu} =
should be available, via some *two-dimensional rule* which allows us to lif=
t rules on selbri to rules on seltau.

I strongly recommend that you read through my notes on formalization and re=
write rules [2]. I will summarize some points based on your specific listin=
g:
* FA: These form a group (each FA rule can be undone, there's a do-nothing =
rule, FA rules compose) and so we only need one rule for introducing/elimin=
ating each of the five FA, plus five more for swapping FA and generating a =
permutation group. Similar reasoning applies to SE.
* CU, KU, terminators in general: We could require that a parse tree is ass=
ociated to each utterance. Then, the rules for terminators each say that a =
particular sort of branch in the parse tree can, because of the neighboring=
 branches, optionally have a CU or KU or etc. You're quite correct that thi=
s is infeasible in Metamath or other embed-your-own-grammar systems that do=
n't know about parse trees.* NA: Should be in a distinct fragment of logic =
from the rest of the core. Lojban is relational, and relational logic is ve=
ry different from Cartesian logic. If we are talking about relations first,=
 rather than quantifiers first, then we should imagine bridi as not being t=
rue or false, but being true in zero or more contexts, with falsity being t=
he special case where zero contexts work. This is all beside the fact that =
topos-based HOL doesn't necessarily have LEM or AOC [3]. {su'o} =3D> {naku =
ro naku} doesn't work except in the special case of Boolean situations.* Mo=
dal logic: Should also be in a distinct fragment. Making modal logic not co=
llapse is something of a magic trick. In a tradition of G=C3=B6del, we imag=
ine that modal logic S4 can embed IPC, the intuitionistic propositional cal=
culus, but in order to make S4 work, we need something like an embedding of=
 S4 into Peano arithmetic. The path for this ends up being IPC =3D> S4 =3D>=
 LP =3D> PA, where LP has the same modal behavior as S4, but whenever somet=
hing is possible, LP carries a *proof* that it is possible. The upshot is t=
hat Lojban doesn't carry around those proofs, and so a lot of work will be =
required to infer them. See [4] or [5] for explanation.
There are totally non-logical particles that must be handled by parsers, li=
ke SA/SI/SU, so once again we have an immediate and satisfying consequence:=
 No, baseline Lojban cannot be totally formalized at the syntactic level in=
 terms of logic, and must be expanded first.
I hope that this is interesting food for thought. Yes, we must immediately =
agree that many parts of the baseline are not formalizable, and provably so=
. But the bulk of the baseline is gismu, and those are definitely related t=
o each other, in addition to coding for relations in their own right. Where=
 those relations can be formalized, we can derive rewrite rules. I haven't =
implemented them in code, but in la brismu, I give Peano arithmetic and bas=
ic manipulation of bridi, as well as a set-theoretic definition of {du} and=
 {lo}; I think that there are concrete useful things to draw from formal ef=
forts.

[0] http://us.metamath.org/mpeuni/mmset.html
[1] https://mw.lojban.org/papri/seljvajvo[2] https://github.com/MostAwesome=
Dude/brismu/[3] https://en.wikipedia.org/wiki/Diaconescu%27s_theorem[4] htt=
ps://sartemov.ws.gc.cuny.edu/files/2013/01/Vienna2011-FOLP.pdf[5] https://w=
ww.youtube.com/watch?v=3DRfSYN5wEW5U[6] https://math.stackexchange.com/ques=
tions/1493341/what-exactly-did-hermann-weyl-mean[7] https://ncatlab.org/nla=
b/show/allegory


On Thursday, April 1, 2021 at 6:03:32 PM UTC-7 Mike S. wrote:

Greetings Corbin,
On Thu, Apr 1, 2021 at 11:08 AM Corbin Simpson <mostawe...@gmail.com> wrote=
:

Hey all,
Time for the sort-of-annual reminder that Lojban falls far short of its goa=
ls. I'll spell out an explicit recipe for achieving those goals.

Suppose that Lojban were logical; that is, suppose that it has a logic [0].=
 A logic has three components:
* A collection of letters which form a collection of words* A grammar which=
 indicates whether a sequence of words is a well-formed sentence* A collect=
ion of rewrite rules which each match sequences of words within well-formed=
 sentences and replace them with new sequences of words which are still wel=
l-formed

What sort of rewrite rules do you mean?=C2=A0 Are you talking about the tra=
nsformation rules of propositional logic, for example, given "P and Q" conc=
lude "P" (i.e. conjunction elimination)? Those sorts of rules are just the =
tip of the iceberg for something like Lojban.

 If you are talking about the total collection of possible rewrite rules, i=
ncluding trivial ones, that could be posited for Lojban, then I suspect tha=
t the collection size would be staggering -- off the top of my head: within=
 clauses, you can reorder terms and the matrix predicate using FA; dependin=
g on context, you can alternate CU and KU and other terminators; again, dep=
ending on context, you can sometimes move NA KU (at least thanks to Xorlo r=
ules you can) and sometimes not, and of course, su'o can be rewritten as na=
ku ro naku; there are bucket loads of particles which can interact with eit=
her clauses or more locally that have some modal-logic effect.=C2=A0 Even i=
f you could sort out all the scope issues, sorting out the semantics would =
not be easy.=C2=A0 Then there is the actual lexicon; in general any predica=
te might have one or more equivalent decompositions (given x1 is a mother c=
onclude x1 is a female parent) and probably has one or more hypernymic repl=
acements (given x1 is a cat, conclude x1 is a feline, or carnivore, or mamm=
al, or vertebrate, or ...).=C2=A0 Finally there is the (non-)compositional =
nature of tanru, the centerpiece of Lojban's semantics.=C2=A0 Thankfully, i=
n practice most tanru are hyponyms of the tertau, so we can be relatively s=
ure a xekri mlatu is a cat, though we can't be fully sure it's a black one,=
 because "je" is not necessarily to be presumed (bizarrely to me).

I don't see how one could go about being totally thorough in specifying rew=
rite rules, and I am not sure it's even possible.=C2=A0 But maybe you have =
something much more focused in mind -- like a fragment of the full Lojban l=
anguage that would be easier to manage.=C2=A0 That might work. I don't know=
.
Best,-Mike


--=20
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lojban/32cb2274-7e23-4680-91f7-eb21fda4ae7cn%40googlegroups.com.
 =20

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<html><head></head><body><div class=3D"ydpc27f324ayahoo-style-wrap" style=
=3D"font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px=
;"><div></div>
        <div dir=3D"ltr" data-setdir=3D"false">Fascinating. &nbsp;But since=
 it is totally locked in to the structure (or lack of it) of Lojban, it is =
ultimately uninteresting. &nbsp;The real question is to figure out what the=
 structure of Lojan should be, given the structure of Language. &nbsp;And, =
since that is not yet given, except very vaguely, that becomes the real que=
stion. &nbsp;I think that, if the language question is answered, the Lojban=
 (or whatever it wil finally be called) question will fall into place quite=
 directly (though not easily). &nbsp;But, since no one in this group is wor=
king on the basic problem, I don=E2=80=99t see the point of patching the le=
aky boat with more soluble paper.</div><div><br></div>
       =20
        </div><div id=3D"yahoo_quoted_8359563926" class=3D"yahoo_quoted">
            <div style=3D"font-family:'Helvetica Neue', Helvetica, Arial, s=
ans-serif;font-size:13px;color:#26282a;">
               =20
                <div>
                    On Friday, April 2, 2021, 06:48:21 AM CDT, Corbin Simps=
on &lt;mostawesomedude@gmail.com&gt; wrote:
                </div>
                <div><br></div>
                <div><br></div>
                <div><div id=3D"yiv5206325766"><div><div>Hi Mike,</div><div=
><br clear=3D"none"></div><div>While you're correct that the number of rule=
s will not be ~10, like in a typical logic, but more like ~10,000; I do not=
 find this to be a serious obstacle. Metamath [0] has tens of thousands of =
handwritten derivations, and a machine can check that they are well-formed =
and valid proofs in only a few seconds. I think that the main difficulty is=
 in composing the rules in the first place.</div><div><br clear=3D"none"></=
div><div>The semantics I recommend for Lojban is a fragment of second-order=
 logic (SOL). This embeds cleanly into HOL. Proof search is infeasible, but=
 that is typical of programming languages; rather than hypernymy getting in=
 the way of proof search, hypernymy offers many choices for folks writing i=
n Lojban to express themselves with nuance.</div><div><br clear=3D"none"></=
div><div>There exist at least two gismu, {dugri} and {tenfa}, which address=
 the same underlying relation. As an immediate and very satisfying conseque=
nce, Lojban cannot have a normal form without some arbitrary violence [6] t=
o the baseline, in the form of a choice which well-orders the gismu. (We co=
uld go alphabetically, of course.)<br clear=3D"none"></div><div><br clear=
=3D"none"></div><div>Many words have been spilled on tanru. To be brief, wr=
iting (=3D&gt;) for implication, I recommend the principles that:</div><div=
><br clear=3D"none"></div><div>* Each lujvo =3D&gt; each implied seljvajvo =
[1] from its terbri<br clear=3D"none"></div><div>* Each lujvo =3D&gt; the t=
anru it was made from</div><div>* Each tanru =3D&gt; its tertau</div><div><=
br clear=3D"none"></div><div>So, for example, from {nanbymlatu} "catloaf; c=
at sitting in a loaf shape" we could conclude {mlatu} "cat". Similarly, fro=
m {xekri mlatu} "black cat" we could conclude {mlatu}. It is okay that adje=
ctives are vague; they still constrain what's logically possible, and that =
is enough.</div><div><br clear=3D"none"></div><div>Note also that, borrowin=
g a bit of category theory, we should expect some allegory-like [7] behavio=
r here. Specifically, if we imagine the (hypothetical!) rule that {xekri} =
=3D&gt; {skari}, then {xekri mlatu} =3D&gt; {skari mlatu} should be availab=
le, via some *two-dimensional rule* which allows us to lift rules on selbri=
 to rules on seltau.<br clear=3D"none"></div><div><br clear=3D"none"></div>=
<div>I strongly recommend that you read through my notes on formalization a=
nd rewrite rules [2]. I will summarize some points based on your specific l=
isting:</div><div><br clear=3D"none"></div><div>* FA: These form a group (e=
ach FA rule can be undone, there's a do-nothing rule, FA rules compose) and=
 so we only need one rule for introducing/eliminating each of the five FA, =
plus five more for swapping FA and generating a permutation group. Similar =
reasoning applies to SE.<br clear=3D"none"></div><div>* CU, KU, terminators=
 in general: We could require that a parse tree is associated to each utter=
ance. Then, the rules for terminators each say that a particular sort of br=
anch in the parse tree can, because of the neighboring branches, optionally=
 have a CU or KU or etc. You're quite correct that this is infeasible in Me=
tamath or other embed-your-own-grammar systems that don't know about parse =
trees.</div><div>* NA: Should be in a distinct fragment of logic from the r=
est of the core. Lojban is relational, and relational logic is very differe=
nt from Cartesian logic. If we are talking about relations first, rather th=
an quantifiers first, then we should imagine bridi as not being true or fal=
se, but being true in zero or more contexts, with falsity being the special=
 case where zero contexts work. This is all beside the fact that topos-base=
d HOL doesn't necessarily have LEM or AOC [3]. {su'o} =3D&gt; {naku ro naku=
} doesn't work except in the special case of Boolean situations.</div><div>=
* Modal logic: Should also be in a distinct fragment. Making modal logic no=
t collapse is something of a magic trick. In a tradition of G=C3=B6del, we =
imagine that modal logic S4 can embed IPC, the intuitionistic propositional=
 calculus, but in order to make S4 work, we need something like an embeddin=
g of S4 into Peano arithmetic. The path for this ends up being IPC =3D&gt; =
S4 =3D&gt; LP =3D&gt; PA, where LP has the same modal behavior as S4, but w=
henever something is possible, LP carries a *proof* that it is possible. Th=
e upshot is that Lojban doesn't carry around those proofs, and so a lot of =
work will be required to infer them. See [4] or [5] for explanation.</div><=
div><br clear=3D"none"></div><div>There are totally non-logical particles t=
hat must be handled by parsers, like SA/SI/SU, so once again we have an imm=
ediate and satisfying consequence: No, baseline Lojban cannot be totally fo=
rmalized at the syntactic level in terms of logic, and must be expanded fir=
st.</div><div><br clear=3D"none"></div><div>I hope that this is interesting=
 food for thought. Yes, we must immediately agree that many parts of the ba=
seline are not formalizable, and provably so. But the bulk of the baseline =
is gismu, and those are definitely related to each other, in addition to co=
ding for relations in their own right. Where those relations can be formali=
zed, we can derive rewrite rules. I haven't implemented them in code, but i=
n la brismu, I give Peano arithmetic and basic manipulation of bridi, as we=
ll as a set-theoretic definition of {du} and {lo}; I think that there are c=
oncrete useful things to draw from formal efforts.<br clear=3D"none"></div>=
<div><br clear=3D"none"></div><div>[0] http://us.metamath.org/mpeuni/mmset.=
html<br clear=3D"none"></div><div>[1] https://mw.lojban.org/papri/seljvajvo=
</div><div>[2] https://github.com/MostAwesomeDude/brismu/</div><div>[3] htt=
ps://en.wikipedia.org/wiki/Diaconescu%27s_theorem</div><div>[4] https://sar=
temov.ws.gc.cuny.edu/files/2013/01/Vienna2011-FOLP.pdf</div><div>[5] https:=
//www.youtube.com/watch?v=3DRfSYN5wEW5U</div><div>[6] https://math.stackexc=
hange.com/questions/1493341/what-exactly-did-hermann-weyl-mean</div><div>[7=
] https://ncatlab.org/nlab/show/allegory<br clear=3D"none"></div><div><br c=
lear=3D"none"></div><br clear=3D"none"><div class=3D"yiv5206325766gmail_quo=
te"><div class=3D"yiv5206325766gmail_attr">On Thursday, April 1, 2021 at 6:=
03:32 PM UTC-7 Mike S. wrote:<br clear=3D"none"></div><blockquote class=3D"=
yiv5206325766gmail_quote" style=3D"margin:0 0 0 0.8ex;border-left:1px solid=
 rgb(204, 204, 204);padding-left:1ex;"><div dir=3D"ltr"><div>Greetings Corb=
in,</div><div class=3D"yiv5206325766gmail_quote"></div></div><div dir=3D"lt=
r"><div class=3D"yiv5206325766gmail_quote"><div class=3D"yiv5206325766gmail=
_attr" dir=3D"ltr"><br clear=3D"none"></div><div class=3D"yiv5206325766gmai=
l_attr" dir=3D"ltr">On Thu, Apr 1, 2021 at 11:08 AM Corbin Simpson &lt;<a r=
el=3D"nofollow noopener noreferrer" shape=3D"rect">mostawe...@gmail.com</a>=
&gt; wrote:<div class=3D"yiv5206325766yqt6317348826" id=3D"yiv5206325766yqt=
fd77373"><br clear=3D"none"></div></div><div class=3D"yiv5206325766yqt63173=
48826" id=3D"yiv5206325766yqtfd19035"><blockquote class=3D"yiv5206325766gma=
il_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,2=
04,204);padding-left:1ex;">Hey all,<div><br clear=3D"none"></div><div>Time =
for the sort-of-annual reminder that Lojban falls far short of its goals. I=
'll spell out an explicit recipe for achieving those goals.<br clear=3D"non=
e"></div><div><br clear=3D"none"></div><div>Suppose that Lojban were logica=
l; that is, suppose that it has a logic [0]. A logic has three components:<=
/div><div><br clear=3D"none"></div><div>* A collection of letters which for=
m a collection of words</div><div>* A grammar which indicates whether a seq=
uence of words is a well-formed sentence</div><div>* A collection of rewrit=
e rules which each match sequences of words within well-formed sentences an=
d replace them with new sequences of words which are still well-formed</div=
></blockquote><div><br clear=3D"none"></div></div></div></div><div class=3D=
"yiv5206325766yqt6317348826" id=3D"yiv5206325766yqtfd34286"><div dir=3D"ltr=
"><div class=3D"yiv5206325766gmail_quote"><div>What sort of rewrite rules d=
o you mean?&nbsp; Are you talking about the transformation rules of proposi=
tional logic, for example, given "P and Q" conclude "P" (i.e. conjunction e=
limination)? Those sorts of rules are just the tip of the iceberg for somet=
hing like Lojban.<br clear=3D"none"></div><div><br clear=3D"none"></div><di=
v> If you are talking about the total collection of possible rewrite rules,=
 including trivial ones, that could be posited for Lojban, then I suspect t=
hat the collection size would be staggering -- off the top of my head: with=
in clauses, you can reorder terms and the matrix predicate

 using FA; depending on context, you can alternate CU and KU and other term=
inators; again, depending on context, you can sometimes move NA KU (at leas=
t thanks to Xorlo rules you can) and sometimes not, and of course, su'o can=
 be rewritten as naku ro naku; there are bucket loads of particles which ca=
n interact with either clauses or more locally that have some modal-logic e=
ffect.&nbsp; Even if you could sort out all the scope issues, sorting out t=
he semantics would not be easy.&nbsp; Then there is the actual lexicon; in =
general any predicate might have one or more equivalent decompositions (giv=
en x1 is a mother conclude x1 is a female parent) and probably has one or m=
ore hypernymic replacements (given x1 is a cat, conclude x1 is a feline, or=
 carnivore, or mammal, or vertebrate, or ...).&nbsp; Finally there is the (=
non-)compositional nature of tanru, the centerpiece of Lojban's semantics.&=
nbsp; Thankfully, in practice most tanru are hyponyms of the tertau, so we =
can be relatively sure a xekri mlatu is a cat, though we can't be fully sur=
e it's a black one, because "je" is not necessarily to be presumed (bizarre=
ly to me).<br clear=3D"none"></div><div><br clear=3D"none"></div><div>I don=
't see how one could go about being totally thorough in specifying rewrite =
rules, and I am not sure it's even possible.&nbsp; But maybe you have somet=
hing much more focused in mind -- like a fragment of the full Lojban langua=
ge that would be easier to manage.&nbsp; That might work. I don't know.</di=
v><div><br clear=3D"none"></div><div>Best,</div><div>-Mike<br clear=3D"none=
"></div><br clear=3D"none"></div></div>
</div></blockquote></div><div class=3D"yiv5206325766yqt6317348826" id=3D"yi=
v5206325766yqtfd17526">

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