A Proposal Regarding Logical Connectives in Vulcan I Rob Zook Wed, 10 Dec 1997 18:17:43 -0600 Hi all, I've been trying to figure out how to flesh out the selection of logical operators in Vulcan and think I have come up with something useful. I figure out what was lacking by thinking about how to express all possible two operand truth tables. While working out the range of possible truth tables I found sixteen total. But six of them have no relevance yet, since they represent the most basic forms of syllogistic arguments. Two represent tautological arguments, and contradictory arguments: Tautology Contradiction ----------- --------------- TT=T TT=F TF=T TT=F FT=T TT=F FF=T TT=F The next two can be represented in English by the phrases, "X whether or not Y", and "whether or not X, Y". The truth tables look like this: X whether or not Y whether or not X, Y ------------------ --------------------- TT=T TT=T TF=T TF=F FT=F FT=T FF=F FF=F The first one represents arguments called "affirming the antecedent", and the second represents arguments called Modus Ponens. Two other tables represent the negation of the above two: !(X whether or not Y) !(whether or not X, Y) ----------------------- ------------------------- TT=F TT=F TF=F TF=T FT=T FT=F FF=T FF=T Arguments of the forms Modus Tollens, and "denying the antecedent". The remaining ten all involve the logical operators of symbolic logic. Prepositional calculus has five main operations: !X, X OR Y, X AND Y, X --> Y, X <--> Y (negation, disjunction, conjunction, material implication, and material equivalence, respectively). We lack a couple of those operators and I would like to propose a couple of Vulcan particles for them: /ek/, and /^m/, for the implication and equivalence operators respectively. Working out the possibilities came much more easily with truth tables than with English statements, and I don't know if one can express some of the following truth tables in English. However, given the acceptance of my proposed terms, and the ones we know, I have some speculations on the possibilities: X'aj Y'aj X'ong Y'ong X'ek Y'ek X'^m Y'^m ----------- ------------- ----------- ----------- TT=T TT=T TT=T TT=T TF=T TT=F TF=F TF=F FT=T TT=F FT=T FT=F FF=F TT=F FF=T FF=T We have already discussed phrases of the form X'aj Y'aj and X'ong Y'ong: qa kya'aj qa nikya'aj, and Spockong Kirkong. A phrase of the form X'ek Y'ek would resemble an English phrase like "X only if Y". A phrase of the form X'^m Y'^m would appear in English like "X if and only if Y". Naturally, adding ni to both particles would negate the entire expression: X'niaj Y'niaj X'niong Y'niong X'niek Y'niek X'ni^m Y'ni^m --------------- ----------------- --------------- --------------- TT=F TT=F TT=F TT=F TF=F TT=T TF=T TF=T FT=F TT=T FT=F FT=T FF=T TT=T FF=F FF=F Some more interesting possibilities can be drawn up, when you only negate one of the inputs to the operator: niX'aj Y'aj X'aj niY'aj niX'ong Y'ong X'ong niY'ong ------------- ------------- --------------- --------------- TT=T TT=T TT=F TT=F TF=F TF=T TF=F TF=T FT=T FT=F FT=T FT=F FF=T FF=T FF=F FF=F From the above table I would say we should probably not consider niX'aj Y'aj and X'ong niY'ong valid usages since they duplicate more simply expressed logic: X'ek Y'ek and X'niek Y'niek, respectively. Interestingly enough, only X'niek Y'niek expresses a unique negative expression with /ek/ and not one like niX'ek Y'ek. Since the latter has the same truth table as X'niong Y'niong. The same is true whether or not you negate one of the inputs to the operator or both, the result will duplicate one of the a fore mentioned truth tables. Even more interesting things happen if you try and negate an /^m/ expression. The truth tables of X'ni^m Y'ni^m, niX'^m Y'^m, and X'^m niY'^m work out exactly the same. So it makes sense to only allow X'ni^m Y'ni^m as valid logic and grammar. I was originally looking at Lojban for a model with these, but given how much Lojban grammar differs from Vulcan, I had to go out to the web in search of information on symbolic logic. Luckily I found a great site if any of you want to brush up on your logic. The University of Newberry in the Caribbean has a completely on-line course, roughly equivalent to a normal College level "Intro to Logic" class. Very complete (much more so than the sorry excuse I got at a community college). You can find it at: http://www,newberry,edu/acad/phil/p110/index,htm Next post I'll talk about a proposal concerning prepositional connectives. Later on I intend to make some more proposals regarding mathematical particles, and a more elaborate and precise tense-aspect system. Rob Z. -------------------------------------------------------- Tis an old maxim in the schools, That flattery 's the food of fools; Yet now and then your men of wit Will condescend to take a bit. --- Johnathon Swift, Cadenus and Vanessa.