No, trival= ent (and other multivalent) logic does not deal with possible worlds, it is= entirely cisworld, not transworld. You could combine the two, allowi= ng multivalence in each possible world and perhaps even get some explanatio= ns of one logic in terms of the other, e.g, that a sentence gets the = value 1 in a world just in case it got the value 2 in some world alte= rnate to that one. But multivalent logics do not depend on such= notions, nor reflect them very well at all (the metatheorem just cited doe= sn't go over to a theorem very well).

"Possible worlds" co= vers a multitude of different systems, not all of which can be conveniently= brought into a single scheme, the Lewis series, say, or the slightly more = generous Kripke one, or the Prior tense-based sets. Some things are common to all (possible worlds, I suppose, for one) but techniques app= ropriate in one area, temporal modalities, say, do not apply in deontic or = epistemic modalities nor in the various subjunctive realms: fiction, repres= entation, contrary-to-fact conditionals, etc. For one major example, the ro= le of the "real world" (the world of primary evaluation) in very different = in these, critical in some cases, irrelevant in others, one world among man= y in still others. Similarly, the metrics which may be laid upon the = the world-connecting vectors, have a variety of different rules, ranging fr= om highly complex to non-existent. The genesis of the possible worlds= is important in some cases, irrelevant (indeed, unaskable) in others. Lojb= an provides AT MOST a way of starting to talk in some of these ways, but no= thing like the a fully functioning language for any of them.

From:<= /b> Gleki Arxokuna <gleki.is.my.name@gmail.com>
To: lojban@googlegroups.com
Sent: Sunday, August 5, 2012 12:16 P= M
Subject: [lojban] Re= vising mu'ei and CAhA once again. Possible worlds.

Continuation of http://www.lojban.org/tiki/mu= 'ei
Note:This topic should be analysed from the Trivalent logic p= oint of view as the latter also deals with Possible worlds.
But l= et's get started with more simple stuff.
mu'ei has always been a = problem for me. Although the wiki was simple in describing it I felt someth= ing incomplete or illogical there.

Luckily, Lojban= istan has some authority and one can always ask how others solve the same p= roblem.
Here is the log.
<gleki> Do you use mu'ei in rea= l life? Do you have any thoughts of making a more generalised abstraction t= hat will include both mu'ei and ba'oi?
<robin>I did = for a bit and then stopped; I just use {da'i} tricks now.
= <gleki>!!! just da'i or pada'i, su'oda'i, roda'i? how can you distinguish between ba'oi and mu'ei then?
<robin>I = don't find ba'oi useful at all. Just da'i.
<gleki>bu= t how can we distinguish two meanings? i just wanna some examples how we ca= n use da'i for each case. If i can't use conditionals then i ca= nt speak this language. Conditionals are the basics. <= i>What are your solutions for su'omu'ei, romu'ei, mu'ei. I can = clearly see differences in their meaning important when speaking. = Regardless the theory of alternate realities behind MUhEI I need words w= ith such semantics. ko sidju mi
<robin>S= o use mu'ei ? There's nothing wrong with them. su'o mu'ei is clearly ka'e. = I have no idea what use ro mu'ei has; it looks totally pointless to me. Erm= , as a bridi tag; as a sumti tag it's fine. Looking at http://www.lojban.or= g/tiki/mu'ei , for "If the train breaks down I'll be late" is {da'i mi lerci ri'a lo nu le trene cu spofu} "If the train breaks do= wn I might be late" is not a structure I usually have to produce, but if I = did I would just use cumki ; {lo nu mi lerci cu cumki lo nu le trene cu spo= fu}

So having this absolution gra= nted from lojbo nolraitru I started revising mu'ei.
Here is w= hat I came up with.
(if you can't see the image look here).

We have two layers. One describes alternate (possible wo= rlds). And it's {ka'e}.
If you have balls of one color only there= are no alternate worlds. i.e. only bag in the middle has more than one out= put at M-level.
Therefore I opine that mu'ei is not a good cmavo = as it's trying to express two levels and therefore two meaning at once. But= cmavo should express one meaning each (being more close to semantic prims)= .

Strangely enough {pu'i} was out of consideration= on mu'ei pages on lojban.= org wiki. That's why mu'ei scheme is not complete and comprehensive.

Other issues including unsettled.
r= omu'ei is absurd.
bi'ai is described as naka'ena which in my sche= me is equal to {ca'a}. But actually in the examples from the wiki bi'ai is = used more like {pu'i}. In any case it's meaning is covered by the existing cmavo.
ba'oi has extra meaning of alternate world identical to T= his World up to the present. This meaning is yet to be defined using new cm= avo if my criticism of mu'ei is accepted.
da'i and va'o look like= non-logical conditionals. Their meaning is out of my understanding. But I'= m gonna use da'i more like Robin in those cases when I'm not sure what alte= rnate-world-cmavo to use or in order to reach ambiguity.
ka'e is = used more like an abbreviation of kakne. If the latter meaning of ka'e is f= ixed we need to find another cmavo for that purpose (for A-level).
naka'e has no cmavo for the output at M-level. Luckily naka'e is short en= ough to be used on it's own.

Conclusion.
mu'ei is not needed. If you wanna describe potential i.e. alternate= worlds at A-level use naka'e, ka'e or naka'ena=3Dca'a.
If in pos= sible worlds some balls are black and some are white then it's ka'e that can result either in nu'o or in pu'i.
You can use all those= cmavo as sumtcita as well which staisfies the need in most conditional sen= tences
(conditionals are sentences like "If I hadn't swum I= would have been healthy" or similar).
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