What can be disagreed upon

This is a continuation of the article entitled “What must be agreed upon”, in which two individuals have a discussion, whereafter a transcript appears that a third party is invited to interpret. The transcript consists of a number of posits, for example ({(J42, girlfriend), (B43, boyfriend)}, official, 2019) and ({(J42, nickname)}, Jen, 1988). The syntax of a posit is described as a triple, where the first position is occupied by a set of ordered pairs, each pair being an identity and a role. The set is followed by a value and time point, which both may be imprecise in nature. What must be agreed upon is the syntax of the posit and the semantics of what it expresses. That sums up the conclusions of the earlier article.

Given the title of this article, let us follow up by investigating disagreements, and here comes an important distinction. Even if you understand what a posit is saying, it doesn’t imply that you believe in what the posit is saying. Many different opinions are certainly held towards a statement such as “We are alone in the universe”. So, if we want to talk about posits in the language of #transitional modeling, the posit itself must be given an identity. To talk about ({(J42, girlfriend), (B43, boyfriend)}, official, 2019) we give it the identity P1 and ({(J42, nickname)}, Jen, 1988) will be P2. The identities make it possible to create new posits that talk about other posits; meta-posits if you like.

If posits that talk about other posits live alongside posits that talk about other things, we cannot allow for any confusion with respect to the roles. We will therefore reserve roles for our purposes, say the strings ‘posit’ and ‘determines confidence’. An assertion is a posit exemplified by ({(P1, posit), (J42, determines confidence)}, 0.8, 2019-04-05). The interpretation is that Jennifer (J42), since 2019-04-05, expresses a confidence of 0.8 with respect to if her girlfriend/boyfriend status with B43 was official since 2019 (P1). Similarly ({(P1, posit), (B43, determines confidence)}, -1, 2019-04-05). We will see that those confidence numbers reveal a big conflict!

Confidences, at lease those found in our assertions, fall within the [-1, 1] interval. The mapping between how something is expressed in natural language and the numerical confidence is fuzzy. But, let us assume that 0.8 corresponds to “very likely”. Then Jennifer is saying that it is very likely that B43 officially became her boyfriend in 2019. The twist in the plot is that the boyfriend is of a very different opinion. On the negative scale of confidences, certainty towards the opposite is expressed, and -1 is “completely certain of the opposite”. More precisely, this is equivalent to being completely certain of the complement of a value. In other words, the boyfriend is completely certain, with confidence value 1, of the posit ({(J42, girlfriend), (B43, boyfriend)}, anything but official, 2019).

Tucked in between is a confidence of 0, which we call “complete uncertainty”. Let us assume that the boyfriend is clueless, and instead asserted ({(P1, posit), (B43, determines confidence)}, 0, 2019-04-05). This is interpreted as the boyfriend having no clue whatsoever if P1 is a truthful posit or not. Perhaps memory is failing or the boyfriend chose to forget. Assertions with confidence give us a powerful machinery to express differences of opinon. To recap, confidence 1 means certain of one particular value, -1 certain it’s a value different from one particular value, and 0 that it could be any value whatsoever. Values in between express confidence to a given degree.

The first article mentioned the unlikeliness of Jennifer eternally being in a good mood. There will come a time when her mood is different. Likely when she finds out what her boyfriend is asserting. At that point, maybe the recollection of her boyfriend is better, and he changes his mind. Circumstances definitely change over time, but we haven’t yet seen change in action. This will be the topic of the next article, entitled “What will change and what will remain”.

The observant reader will notice that assertions here are slightly different from in the paper “Modeling conflicting, uncertain, and varying information”. There the assertion is an actual construct, a predicate, different from the posit. Here the assertion is a meta-posit built around a semantical reservation. The reasoning behind the different approach is that if assertions are expressed as posits, they can be talked about as well using another layer of posits; a kind of über-meta-posits.

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Lars Rönnbäck

Co-developer of the Anchor Modeling technique. Programmer of the online modeling tool. Site maintainer. Presenter and trainer.

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