(Originally appeared in Lognet 98/1)
We propose that Loglan incorporate Kripke-style alternative-worlds modal logic into the Loglan tenses in PA. In order to do this, we propose four new words:
1. The first new word is kui in PA. Kui has no good English translation. It stands for the relationship between a possible world or event and the original world from which the first is possible. In Kripke-style logic this relation is known as the accessibility relation. The Loglan meaning of kui is determined by the rules for replacing it with a predicate.
The eliminative predicate for kui is blikui (see definition below); the elimination transformations for kui are:
Ba kui preda.
=> Ba preda kui ti.
=> Lepo ba preda guo blikui ti.
and
Ba kui be preda.
=> Lepo ba preda guo blikui be.
and
Ba preda be kui bo.
=> Lepo ba preda be guo blikui bo.
Note that kui be and kui bo are sentence modifiers, and that the modified sentence gets wrapped in Lepo ... guo.
The best English translation is context dependent but can usually be built using possible/accessible (from), as illustrated by these sample usages:1
Mi kui hapci.
== Mi hapci kui ti.
== Lepo mi hapci guo blikui ti.
== The event of my happiness is accessible from this (world).
== My happiness is possible from here.
== It is possible that I am happy.
== I might be happy.
Mi hapci kui lepo mi bragai.
== Lepo mi hapci guo blikui lepo mi bragai.
== The event of my happiness is accessible from (world(s)) where the event is I am king.
== My happiness is possible in (a) world(s) where I am king.
== I might be happy were I the king.
Note that this last example does not mean that any world where I am king is one where I am happy; it only means that a world where I am king makes a world where I am happy accessible. That is, it does not say I would be happy were I the king. Ways to say this last occur below.
Loglan has a unique logical mechanism for quantifying tenses, the NI+PA forms. Quantified kui makes some fine distinctions possible that are inexpressible in English. These are illustrated by sukui and rakui.2 When eliminating a NI+kui form, its NI is used to form a cardinal predicate, NI+ra, which is then used to modify the eliminative predicate, blikui. This allows the specification of varying degrees of accessibility.
Mi sukui hapci.
== Mi hapci sukui ti.
== Lepo mi hapci guo sura blikui ti.
== The event of my happiness is a singly-or-more kind-of accessible from this.
== My happiness occurs in some possible world.
== My happiness is possible.
== I might be happy.
Remember the difference between plain PA and quantified NI+PA forms. Unquantified forms carry an implicit qualification by the intent of the speaker and have no definite quantity. So Mi kui hapci means I am happy in the accessible world or worlds I intend and Mi sukui hapci means I am happy in at least one possible world I intend. This subtle distinction is inexpressible in English short of long circumlocutions like these.
Mi rakui hapci.
== Mi hapci rakui ti.
== Lepo mi hapci guo rara blikui ti.
== The event of my happiness is a universal-kind-of accessible from this.
== My happiness occurs in all possible worlds.
== My happiness is necessary. (i.e. my unhappiness is impossible)
Note that the philosopher’s possible (= 
) is sukui ti and the philosopher’s necessary (= ![[N]](necessary-glyph.gif)
) is rakui ti, with the caveat that philosophers use sentence-forming modifiers and Loglan PA words imbed within sentences. The NI+PA mechanism in Loglan is logically very powerful, much more so than in any previous speakable language.
2. The second new word is blikui, the predicate which explicates kui. The definition of blikui is:
blikui <blicu kunci = possibly-related>
... is (occurs in a world/context/setting/possibility) related to ... by accessibility relation ...
blikui is a predicate with three slots: X blikui Y Z.
The first, X, is an event or predication.
The second, Y, is a reference that determines a possible world.
The third, Z, is an accessibility relation.
The sequence of slots is important for the grammar of kui to work correctly.
3. The third new word is not really new. We propose promoting feu from the discursives to PA. The current definition is feu <fekto> LW L4 75 1.0 (av) in fact/actually, a discourse operator (UI). We propose changing it to allow an argument so that feu ba means, in fact, in worlds/situations/realities where ba exists.
Note that kui relates possible worlds which might be different, while feu says that two worlds are really one. In much the same way, pa and fa relate two times while na says that two times are really one.
Kripke-style formal logics have no operator corresponding to feu. So why does Loglan need feu? The reason is complex, involving the difference between sentence operators versus grammar within sentences. Let us illustrate with an example:
Mi kui hapci.
Mi hapci kui ti.
== It is possible that I am happy.
== (I am happy).
Notice that kui ti is inside the sentence while the logically equivalent is not. Together with the grammar of PA, the use of kui leaves a logical hole: kui must mean possible from where in order for Mi kui hapci to mean what we propose, leaving the question of how to say just possible where as in My happiness is possible where I am King. (One of several meanings for I’d be happy were I King.) Feu fills this logical hole.
The eliminative predicate for feu is feorkui (see definition below); the elimination transformations for feu are:
Ba feu preda.
=> Ba preda feu ti.
=> Lepo ba preda guo feorkui ti.
and
Ba feu be preda.
=> Lepo ba preda guo feorkui be.
and
Ba preda be feu bo.
=> Lepo ba preda be guo feorkui bo.
Some sample usages are:
Mi feu hapci.
== Mi hapci feu ti.
== Lepo mi hapci guo feorkui ti.
== The event of my happiness is in the same reality as this (world).
== I am happy in this world.
== I am, in fact, happy. (although unhappiness might be possible)
Mi hapci feu lepo mi bragai.
== Lepo mi hapci guo feorkui lepo mi bragai.
== The event of my happiness is in the same world as the event of my being king.
== I am happy in the world where the event is I am king.
== I’d be happy were I king.
Used together with kui, feu specifies which possible worlds contain the kui event. Often, using them both is redundant, merely adding emphasis to the counterfactual nature of the assertion.
Mi kui hapci feu lepo mi bragai.
== Mi hapci kui ti feu lepo mi bragai.
== Lepo mi hapci guo blikui je ti ze feorkui je lepo mi bragai.
== The event of my happiness is jointly accessible from this world and also occurs in world(s) where I am king.3
== I am happy in world(s) accessible from here, in realit(y/ies) where I am king.
== I’d be happy were I king.
Combined kui and feu are not always redundant. The logic of some combined usages is mind-expanding.
Mi kui hapci feu ti.
== Mi hapci kui ti feu ti
== Lepo mi hapci guo blikui je ti ze feorkui je ti.
== The event of my happiness is jointly accessible from this world and also occurs in this world.
== My happiness occurs in a world possible from here, a world which is this world.
==I am happy in this world.
==I am happy.
The mutual cancellation is mind-bending but exactly logical. Exactly the same cancellation can occur with pa and na. Mi pa hapci na ti. == Mi hapci pa ti na ti.
NI+PA quantified feu can be mind-expanding also. We suggest some example usages with sufeu and rafeu.
Mi hapci sufeu lepo mi bragai.
== Lepo mi hapci guo sura feorkui lepo mi bragai.
== The event of my happiness is a singly or more kind of reality where the event is I am king.
== I am happy in at least one reality where the event is I am king.
== I could be happy were I a king.
Mi hapci rafeu lepo mi bragai.
== Lepo mi hapci guo rara feorkui lepo mi bragai.
== The event of my happiness is universal kind of reality where the event is I am king.
== I am happy in all worlds where the event is I am king.
== I would be happy were I a king.
The distinction between kui and feu is more subtle and more logical than anything in English. Errors are easy to make, which can be thought of as a problem with this proposal. Alternatively, it can be thought of as a strong point of the proposal. Proper use of kui and feu, especially the NI+PA forms, requires careful use of subtle logic. This ought to produce powerful Sapir-Whorf effects if anything can. A few example usages ought to illustrate this point.
Mi rakui hapci feu lepo mi bragai.
== Mi hapci rakui ti feu lepo mi bragai.
== Lepo mi hapci guo ge rara blikui je ti geu ze feorkui je lepo mi bragai.
== The event of my happiness is jointly a universal kind of accessible from here and also occurs in world(s) where I am king.
== I am happy in all worlds accessible from here, worlds where the event is I am king.
== Were I king, my happiness would be inevitable.
== Necessarily, were I king I would be happy.
Mi sukui hapci feu lepo mi bragai.
== Mi hapci sukui ti feu lepo mi bragai.
== Lepo mi hapci guo ge sura blikui je ti geu ze feorkui je lepo mi bragai.
== The event of my happiness is jointly a one or more kind of accessible from here and also occurs in world(s) where I am king.
== I am happy in some world(s) accessible from here, (a) world(s) where the event is I am king.
== Were I king, my happiness would be possible.
== My being king would make my happiness possible.
Mi kui hapci sufeu lepo mi bragai.
== Mi hapci kui ti sufeu lepo mi bragai.
== Lepo mi hapci guo blikui je ti ze ge sura feorkui je lepo mi bragai.
== The event of my happiness is jointly accessible from here and also is a one or more kind of occurrence in (a) world(s) where I am king.
== My happiness is accessible from here, in some world(s) where the event is I am king.
== My happiness is possible, in fact were I king it might occur.
== Were I king I might be happy.
Do not take the use of could and would too seriously in these examples. A pattern occurs in English in which would corresponds to necessity, to the universal quantifier over possible worlds, while could corresponds to possibility, to the existential quantifier over worlds. Hence rakui and rafeu can often both be translated using would and similarly sukui and sufeu both often correspond to could. Note that the correspondence is not one-to-one in either direction; both would and could have several other meanings.
4. The last word proposed is feorkui, the eliminative predicate for feu. The definition of feorkui is:
feorkui <fekto kunci = factually-related-to>
... is actually related to (occurs in the same world as) ... according to point-of-view/observer/metaphysics/reality ...
Feorkui has three slots: X feorkui Y Z, not by coincidence very similar to those for blikui:
The first, X, is an event or predication.
The second, Y, is a reference that determines a possible world.
The third, Z, determines what counts as a possible world.
Again, the sequence of slots is important for the grammar of feu to work correctly. That is the proposal. A rough draft of a document with more usage examples has been started. Given interest, it could be polished up and supplied. [We are interested; please supply.]
1. A chain of sentences connected by == signs are all mutual translations of each other. The Loglan specimens are in bold and go from the best recommended usage to the most technical explication. The English specimens are in italics and go from the most literal translation to the best colloquial usage.
2. The explication of quantified PA is not a settled issue. For uniformity we are following the rule that, when explicating NI+PA, one modifies the explicating PREDA for the PA word with the cardinal predicate NI+ra.
3. Explication of multiple separate PAs in one sentence requires ze-connected predications applied to one event, the event of the main predication of the sentence. Otherwise there is insufficient connection between the two predicates explicating the two PA words, and things fall apart into two separate assertions. This proposal relies on this feature. Compound PAs, e.g., fafa, on the other hand, seem to require nesting LEPO clauses. This proposal does not include any such compound PA words.
Copyright © 1998 by The Loglan Institute. All rights reserved.