He starts his paper from 1987 [1] with a reference to the PROSPECTOR expert system which was using Bayes rules to handle uncertain knowledge. Then he explains the idea behind probabilistic logic which is used for determine the value of true/false statements in a semantic tree. The probability values are displayed in a 3d box graphically to make the concept clearer for the newbies. He calls the concept

quote: “straightforward generalization of the ordinary true-false semantics”

But something is wrong with the paper. Approximately in the middle of the text, i missed the point why such an alternative logic concept is useful. Isn't it enough to deal with normal yes/no statements which can stored in a Turing machine much easier? Why do we need complicated 3d boxes with a probability landscape?

[1] Nilsson, Nils J. "Probabilistic logic." Artificial intelligence 28.1 (1986): 71-87.


In a practical sense, there is no such thing as perfect information-- if it exists at all, it is rare enough that it is not enough to build useful systems out of. A real, physical system made with real, physical sensors, in a real, physical environment will have practical tolerances which are best modeled as stochastic processes.

In a similar vein, many games involve an element of chance as well. Without probabilistic modeling, it is very hard (I would say impossible) to develop an AI for something as simple as a poker game.

Finally, sticking absolute certainty into models of these systems (where absolute certainty doesn't exist) tends to be in some sense "sticky" where the certain propagates improperly through the rest of the model, making it useless very quickly.

No, in my opinion, the paper is not wrong.

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In the first sentence of the paper, Nilsson states that [s]everal artificial intelligence (AI) applications require the ability to reason with uncertain information. Nothing (well, almost nothing) is ever just true or false, and binary logic is not enough to model a complex world. So we need more powerful means of describing logical relationships that go beyond just true and false.

In his paper, Nilsson presents an extension to normal, binary, logic to allow probabilistic truth values between 0.0 and 1.0 for sentences. This is a more powerful way of logical reasoning, but of course it is also more complex than operating with just binary values.

In essence your question boils down to do we need this?, and I would say yes, we do. Especially with reasoning about things, we often have incomplete information, because we don't know something, or it hasn't happened yet. For this it is very useful to be able to deal with probabilities. This applies to other fields of AI as well.

So, there is nothing 'wrong' with the paper.

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  • $\begingroup$ Here is a misunderstanding visible, what a computer language is. The idea behind a formalized language is, that the statements are executed in a discrete way. The Finite state machine gets an input and produces an output. And if the reality is more complex, the programmer has to figure out how to convert uncertainty into boolean logic. $\endgroup$ – Manuel Rodriguez May 8 '19 at 8:05

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