History: Tsani's Interpretations: Abstractors

Source of version: 16 (current)

This page is part of a series called ((Tsani's Interpretations of Controversial Lojban Grammar|Tsani's Interpretations of Controversial Lojban Grammar)). Any abstractors in Lojban are extremely useful with their current definitions, but with ((The Complete Lojban Language|the book))'s definitions not quite matching the way many abstractors are used in current conversations on IRC, I feel the need to explain the way ((la tsani|I)) use these cmavo, in perhaps what is an attempt to make them, overall, more useful. As for the presence of {ce'u} within these embedded bridi, I adhere to ((ka, du'u, si'o, ce'u, zo'e|these rules)). As for subscripting {ce'u} with {xi} in the event of a {ce'u}-type abstraction being contained within an abstraction, I adhere to the rules of relative clauses as outlined in The Book. That is to say that {ce'uxire} refers to a {ce'u} of the parent abstraction ''even if that abstraction is not {ce'u}-capable'', i.e. a member of {nu} and friends. This is done for the sake of simplicity. Using {ce'u} without a subscript in a {ce'u}-incapable clause ({nu} et al.) is always __incorrect__, ''even if that clause is embedded within a {ce'u}-capable one''. Experimental cmavo proposed in this paper: *du'au LAhE based on {du'u}; converts a text into a bridi *lu'au LAhE based on {lu}; converts a bridi into a text *ce'ai ZOhU based on {ce'u}; denotes a lambda prenex (used to be ce'au) !{nu} and {du'u} These two abstractors constitute the core of this document. Disregarding {su'u}, it is my belief that all abstractions can be expressed using only {nu} and {du'u} (to some degree) and thus that all other abstractors exist only for convenience, or for achieving certain slightly more specific interpretations (as is the case for {jei} and {ni}, described near the end of this document). !!{nu} {nu}, like its gloss suggests, creates an event, which is bounded in spacetime and has various properties such as its duration and its location(s). It is mainly used after sumtcita, such as and most commonly {ca}. ''.i ca lo nu zdani nerkla kei mi co'u cutci dasni -- When I enter my house, I take off my shoes.'' (For additional explanations on {ca} and other tenses and sumtcita, see ((Tsani's Interpretations: Sumti Tags|this)).) There are no circumstances for which a nu-clause should contain {ce'u}; the same goes for {nu}'s friends, {li'i}, {mu'e}, {pu'u}, {za'i}, and {zu'o}. Additionally, a nu-clause should never contain an indirect question. That is to say that a {nu} abstraction must always be "fully applied". See the section on {ka} for an explanation of "application". The "return value" of a nu-clause is inherently a fasnu1. !!{du'u} {du'u} is the predication abstractor, where it differs from {nu} in that {du'u} has an x2, namely the text claiming du'u1. Predications are not are not bound in spacetime and have properties such as sumti being related, type of relationship, and modals and connectives involved. A du'u1 is a sort of class of nu1, such that events are instances of predications. That sparked my idea for ((fasnu2|fasnu2)). There are few brivla that actually use true du'u. In fact, it seems like most of the "facts xN (du'u) about subject xN+1" are actually properties, rather than real predications. For instance, for all uses of {djuno} where the x3 must find its way into the x2 in order to be semantically correct, djuno2 is a property of djuno3, rather than a du'u. More on that in the section about {ka}. {du'u}'s default "return value" is a bridi1, which entails that under my interpretation, bridi1 is a du'u1. A return value that differs from the default is marked using an indirect question: compare {lo du'u do klama}, {lo du'u do klama makau}, {lo du'u do mokau}, and {lo du'u mi jikau do klama}. There are some questions for which the interpretation is strange: consider {lo du'u peikau mi cinba do}[1], {lo du'u fi'akau do cinba fi'akau mi}, {lo du'u mi sexixokau darxi do}, and {lodu'u xokaure'u nu mi cinba do}. There are two particular indirect questions, namely {la'umakau} and {xukau}, that are discussed in the section regarding {jei} and {ni}. Of course, as could be seen in the {fi'akau} example, there's nothing wrong with using multiple indirect questions. As for {peikau}, it glosses "what ''you'' feel about broda" and not "what ''I'' feel about broda". (Okay, it ''could'' mean "what I feel about broda", but only under a {doi mi} context, which is silly.) Some problems arising from ((Tsani's Interpretations: The Superman/Lois Lane Paradox|the Superman/Lois Lane paradox)) prompted the creation of two experimental cmavo, which are useful only under very specific circumstances: {((Tsani's Interpretations: du'au|du'au))} and {((Tsani's Interpretations: lu'au|lu'au))}. Both are members of LAhE and they respectively cast a text into a bridi1 and bridi1 into a text. For example, consider {.i ko'a goi lo du'u mi citka ci lo plise}. {.i mi cusku lu'au ko'a} is equivalent in meaning to {.i mi cusku lo se du'u mi citka ci lo plise}. !{ka} and {si'o} These two abstractors are children of {du'u}, in the sense that it is possible, using only {du'u} to express meanings identical to those of {ka} and {si'o}. I work under the assumption that a du'u-clause containing at least one {ce'u} is equivalent to a ka-clause and that a du'u-clause where all sumti places and explicit modal places are {ce'u} is equivalent to a si'o-clause. !!{ka} Under my interpretation, {ka} is hugely useful, in that it supplants many prior uses of {nu}. In order to properly understand the way that I grasp the property abstraction, it is necessary to understand that Lojban uses a second order logic for this. Consider {bebna = x1 is foolish in property x2} and the example {mi bebna lo ka [ce'u] cinba du'ezo'e}. Readily, we can see that there is a sort of second-degree predication, namely {lo du'u mi cinba du'ezo'e}. This is a process that I call ''application''. Applying a property to a sumti or to sumti means to reduce the property abstraction using {ka} into a predication abstraction using {du'u}. To do so, one must determine the referents of the {ce'u}. For instance, {mi mutce lo ka ce'u tavla do makau} -> {lo du'u mi tavla do makau}. Application is a process handled by the selbri relating the property; the speaker never has to worry about application. In other words, the "property brivla", such as but not limited to {kakne}, {mutce}, {simxu}, {zukte}, {mulno}, {simsa}, and {dunli}, function in a two-step process of applying the property, and then making a claim about the predication that results from the application. Note that as a {du'u} abstraction is called a bridi or proposition, a {ka} abstraction is called a ''function'', where the {ce'u} is/are the parameter(s). !!{si'o} Certainly less useful than {ka}, {si'o} has a specific function that is difficult or irritating to implement with a {du'u} abstraction. Under my interpretation, a sidbo1 __is not__ a {si'o}. I believe that a sidbo1 is simply a property of sibdo2, as understood/created/interpreted by sidbo3. I understand {lo si'o broda} as meaning "what is means to ''broda'', for si'o2" or "the meaning of ''broda'', for si'o2" or "<si'o2>'s interpretation of ''broda''". It turns out that {si'o} as per this definition greatly resembles ((latro'a|latro'a))'s {me'ei}, aka the "Article for abstract predicate sumti," save for that si'o allows for more flexibility. For instance, {lo si'o citka} == {me'ei citka} assuming that the si'o-abstraction contains no implicit makau, which can be a pain. Now, {si'o} can certainly contain for more complex selbri than simple {me'ei} can, because {me'ei} is a LE, but {me'ei} has the uncanny ability of being completely unambiguous as to the true nature of its contents: it's definitely a pure selbri. !{du'u}'s friends: {ni} and {jei} {ni} and {jei} fall into "{du'u}'s friends" category, rather than the "{du'u}'s children category" which encompasses {ka} and {si'o}, due to that there are no required {ce'u} in a ni/jei-abstraction. However, they remain {du'u}'s ''friends'' and __not__ {du'u}'s ''siblings'' due to that a simple {du'u} abstraction can be used to obtain an __almost__ equal meaning. It ''must'' be noted that {ni} and {jei} do have interpretations slightly different from their du'u-equivalents. Like a {du'u} abstraction however, {ni} and {jei} abstractions may contain {ce'u}. !!{ni} A {ni} abstraction is vague. It may extract from the bridi either a pure number, a number ''with units'', or a vague sort of comparable-ish thing. In terms of {du'u}, this is done by means of a sumti indirect question attached to a modal, namely {sela'u} or {la'u}, for the first two possible return values, respectively. These modals stem from {klani} from which {ni} itself stems. Considering that properties are not comparable, but that quantities are, a {ni} abstraction is under my interpretation the correct sumti for the comparison property place of {zmadu}, {mleca}, and (on some occasions) {dunli}. e.g. ''mi zmadu do lo ni ce'u certu lo ka ce'u tavla fo lo lojbo'' "My ability to speak Lojban exceeds yours" !!{jei} The ''truth-value abstraction'' as it's called is in a sense a specialisation of {ni}, rather than of {du'u} itself, considering that the return value of {jei} under my interpretation is a real number in the interval [0, 1]. As numbers are comparable, {jei} abstractions may be used as zmadu/mleca/dunli3, but this is unuseful outside of fuzzy logic contexts. All in all, however, {jei} has extremely few uses. In terms of a {du'u}-approximation, {jei} is similar to {lo du'u xukau broda} !The Pre-application of properties Some places that use {du'u} in Official Lojban, but {ka} under my interpretation may be ''pre-applied'', i.e. applied by the speaker and not the selbri. The most notable instance of pre-application is {djuno}. Under my interpretation, it would be necessary for all {djuno} bridi to be of the type {ko'a djuno lo ka ce'u brode kei ko'e}, which is extremely inconvenient. Thus, for the sake of simplicity, preserving backwards-compatibility as much as possible, and not having to use {kei}, using a plain, fully-applied {du'u} is acceptable as a djuno2. If djuno3 is left implicit, it is understood that it is some sumti from the proposition expressed in djuno2. If djuno2 is fully-applied but djuno3 is specified and is not redundant to any explicit or implicit sumti that are present in the djuno2 proposition, it is defined as being the referent of an implicit {ce'u} inside the prenex of the djuno2 proposition. Example of pre-application: {mi djuno lo ka ce'u nelci co citka lo plise kei do}, {mi djuno lo ka do nelci co citka ce'u kei lo plise} -> {mi djuno lo du'u do nelci co citka lo plise} !A list of gismu that I propose should use {ka} This list is ''not'' exhaustive. Typically, when a selbri has an abstraction place in which another of that bridi's sumti must be in order to achieve understandable semantics, that abstraction place is a property of that sumti. Consider the case of {mi kakne lo nu do citka lo plise}. *kakne = x1 is capable of being/doing x2 (ka) under conditions x3 (nu) (It is possible for x2 to be a property of x1 given that x3 occurs/is true) *zukte = x1 employs means x2 (ka) to bring about/cause x3 (nu) (x3 becoming/remaining true is the intentional antecedent of x2 being a property of x1) *cirko = x1 loses property x2 (ka) under conditions x3 (nu) (x2 ceases to be a property of x1 given that x3 occurs/is true; no implication of volition; cf. sisti) *troci = x1 attempts x2 (ka) by actions/method x3 (ka) (x2 becoming/remaining a property of x1 is the result of x3 being a property of x1, ''setese zukte a'i'', no implication of success (x2 __might not__ become a property of x1)) *snada = x1 accomplishes/succeeds at x2 (ka) as a result of attempt x3 (ka) (success version of troci) *fliba = x1 fails at being/doing x2 (ka) (failure version of troci) *sisti = x1 ceases to be/do x2 (ka) (x2 being a property of x1 comes to an end as the result of the volition of x1; volitional cirko; ''snada lo ka cirko'') *zifre = x1 is free to be/do x2 (ka) under conditions x3 (nu) (x1 can acquire or lose property x2, at will, given that x3 occurs/is true) *bilga = x1 is obliged to be/do x2 (ka) by standard/agreement x3 (nu?) (x2 is a property of x1 disregarding the volition of x1 as a result of x3 occurring/being true) *fuzme = x1 is responsible/accountable for action x2 (ka) to judge/authority x3 (x3 recognizes that x2 is a property of x1) *gunka = x1 works/labours at x2 (ka) for purpose/goal/objective x3 (nu) (x3 is the desired antecedent of x2 being a property of x1) *lazni = x1 is lazy at/avoiding work/effort concerning action x2 (ka) *tatpi = x1 is tired/fatigued by effort/work/situation x2 (ka) *surla = x1 is relaxed/relaxing/resting/is at ease at being/doing x2 (ka) *srera = x1 errs in doing/being x2 (ka), erroneous under conditions x3 (nu) by standard x4 (x4 considers x2 being a property of x1 to be an error, regardless of x1's volition, given that x3 occurs/is true) *darsi = x1 shows audacity in doing/being x2 (ka) *virnu = x1 is brave/courageous in doing/being x2 (ka) by standard x3 *bebna = x1 is a fool/idiot/boob at doing/being x2 (ka) *stati = x1 has a talent/aptitude/innate skill for doing/being x2 (ka) *tarti = x1 behaves/conducts oneself as/in manner x2 (ka) under conditions x3 (nu) (x2 is volitionally the property of x1 given that x3 occurs/is true; consider "I'm polite around girls" -> {mi tarti lo ka clite kei tu'a lo ninmu}) *certu = x1 has skill/shows prowess at doing/being x2 (ka) by standard x3 *sutra = x1 is fast/swift at doing/being x2 (ka) *masno = x1 is slow/sugglish at doing/being x2 (ka) *frati = x1 reacts/responds with action x2 (ka) to stimulus x3 (ka) under conditions x4 (nu) (x3 being a property results in x2 being a property of x1 disregarding x1's volition, given that x4 occurs/is true; cf. spuda for a volitional form) *spuda = x1 answers/replies/responds to x2 (ka) with response x3 (ka) (x3 being a property of x1 is a desired result of x2 being a property of x1; ''mi spuda lo ka do teryrei lo du'u xukau ce'uxire kanro kei kei fo lo ka ce'u goi ko'a cusku lo sedu'u ko'a ja'a kanro'' "The answer that I tell you when you ask me how healthy I am is that I'm indeed healthy." As that's extremely wordy, sumti raising becomes a very viable option: {mi spuda tu'a lo du'u xukau kanro kei tu'a lo sedu'u ja'a kanro}) *bredi = x1 is ready/prepared for x2 (ka) *rivbi = x1 avoids/shuns/escapes/skirts [fate] x2 (nu) by action/state x3 (ka) (x2 is __not true/doesn't occur__ as a result of x3 being a property of x1, as per x1's volition) *((Tsani's Interpretations: Bad gismu|zajba)) = x1 is a gymnast at/performs gymnastics feat x2 (ka) *((Tsani's Interpretations: The case against cinse|cinse)) = x1, in activity/state x2 (ka), exhibits sexuality/gender/sexual orientation x3 (ka) by standard x4 *kamni = x1 (mass) is a committee with task/purpose x2 (ka) of body x3 *vecnu (the gimste agrees with me here) = x1 sells x2 (ka) to x3 for price x4 (a money transaction between x1 and x3 (x3 giving money to x1) results in x3 acquiring property x2) Difference between {kakne} and {zifre}: compare {mi kakne lo ka ce'u co'a morsi kei lo ka ce'u goi ko'a pinxe lo vindu be ko'a} and {mi __zifre__ lo ka ce'u co'a morsi kei lo ka ce'u goi ko'a pinxe lo vindu be ko'a}. Where {kakne} says nothing about volition, {zifre} indicates that as a result of the combined truth of zifre3 and zifre1's desire to zifre2, zifre2 can be a property of zifre1. I extend the meaning of zifre to include acquiring and losing the property, ''at will'', so long as zifre3 is in effect. !!Problems with using {ka}; "How do I say X?" Some of you might complain that using these properties instead of events for some gismu, such as {bredi}, makes them less useful, but I argue that a form of sumti raising answers that problem. How to say, under my interpretation, "I'm ready for the end of the world" ? Under official Lojban, let's say that {mi bredi lo nu fanmo pe'a lo munje} glosses the English sentence. Then, ask yourself, "What is that that I'm ready for?" You can't be prepared ''for an event''; you can however be prepared to ''experience'' that event. Thus, I consider {mi bredi lo ka ce'u lifri lo nu fanmo pe'a lo munje}, which is long, but which can be reduced into {mi bredi tu'a lo nu fanmo pe'a lo munje} (yes, it's one of those "I'm raising an event O_o" situations) or into {mi seli'i fanmo pe'a lo munje kei bredi} or into the more afterthought form involving {co}, {mi bredi co seli'i fanmo pe'a lo munje}, as being a better solution. Another notable ka-ification is that of {sisti}, which I differentiate from {cirko} with volition. That is to say that {lo si'o sisti cu si'o zukte lo ka ce'u cirko ce'uxire}. In order to get at the "old" version of sisti, I'd use {zukte fi lo nu xy tolcfa}. {mi tatpi lo nu do krixa} doesn't make any sense, clearly. Y screaming is not a situation that tires X, but X ''experiencing'' Y screaming is. This is another example of a {broda lo kaseli'i brode}. {co} becomes a real jewel as it lets us avoid a lot of description and abstraction boilerplate. Consider the previous example, {zukte fi lo nu tolcfa}. We can readily reduce this into {zukte co tolcfa} (this necessarily resolves into {tolcfa} as zukte3 because a cfari1 is an event and not a property and therefore would be semantically uninterpretable as a zukte2). Similarly, {kakne lo ka broda} can be transformed into {kakne co broda}. This was possible before this ka-revolution, and is thus not an antecedent of my proposal, but I do advocate furthering the use of {co} in order to reduce the number of uses of {lo} and various abstraction markers. For example, consider that {mi ce do simxu lo ka ce'u kansa ce'u lo ka ce'u zgana lo nu lo pendo be vo'a cu dansu je tigni} can be reduced into {mi ce do simxu co kansa co zgana co seke dansu tigni lo vo'a pendo}, a seven word and ten syllable gain, reducing in this case by almost 30% the length of the sentence. Yes, this system involves more words for ''a lot'' of constructs, (if you're a {co}-hater, that is,) but now we have a more consistent type system that lets us pass around properties like so: {mi bredi lo na se kakne be do}, {do djuno lo mi se zifre}. !!Various ideas !!!A Lambda prenex Initially, {ce'u} was meant to be a PA, lambda-quantifying an otherwise logically-quantified variable (the {da}-series). Perhaps it is worth reviving this idea, although slightly modified, in an attempt to fix nested abstractions, which are otherwise messy, what with all the required subscripting. The original idea was for {ka} abstractions to be of the form ''lo ka ce'u da broda da'' (remember, {ce'u} in there is a PA) for a reflexive property, and ''lo ka ce'u da broda ce'u de'' for non-reflexive properties. Let {ce'ai} be a member of ZOhU, denoting a lambda prenex, where all variables are understood to be lambda-quantified: #''lo ka da ce'ai da prami da'' the property of loving oneself. #''lo ka da de ce'ai da broda lo ka di ce'ai de brode di'' In here, de is referring a {ce'uxire}. In this system, we can mix {ce'ai} prenexes with regular {ce'u} without fear. {ce'u} is thus treated as the afterthought form. Using a {ce'ai} prenex more closely parallels lambda calculus from which the description of properties is largely based in this document. It is also possible to mix logically prenexes with lambda prenexes, as even in official Lojban, multiple ZOhU-clauses are permitted: {lo ka da zo'u de ce'ai de se prami da} is "being loved by something/someone". !Some notable formulae ''Note: ''dy. ubu'' is my pet name for the identity property, such that:'' .i ca'e dy. ubu ka ce'u du makau Under this interpretation of abstractors, the following is true: *{ko'a ckaji lo ka ce'u broda} = {ko'a broda} *{ko'a dunli ko'e lo ka ce'u broda} = {ko'a .o ko'e broda} *{ko'a zmadu ko'e lo ka ce'u broda} = {ko'a .enai ko'e broda} *{ko'a zmadu ko'e lo ni ce'u broda} = {lo ni ko'a broda cu zmadu lo ni ko'e broda kei dy. ubu} *{ko'a co'a ckaji lo ka ce'u broda} = {ko'a binxo lo ka ce'u broda} *{ko'a co'u ckaji lo ka ce'u broda} = {ko'a cirko lo ka ce'u broda} *{ko'a sisti lo ka ce'u broda} = {ko'a zukte lo ka ce'u cirko lo ka ce'u broda} *{lo si'o binxo cu si'o tolcri .i je lo si'o cirko cu si'o tolbi'o} And others that I haven't either the time to define or yet determined.