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well the ternary thing about SQL is that it has this NULL/unknown, and it can be demonstrated with the outer joins. Then SQL being a slang of DataLog, which co

by larodi 3y ago

well the ternary thing about SQL is that it has this NULL/unknown, and it can be demonstrated with the outer joins. Then SQL being a slang of DataLog, which comes from Prolog implies Prolog is ternary, no? Indeed Prolog's handling of "unknown" is more procedural than a true ternary logic. So it has slightly different notion. Even though I'm more a Prolog amateur (s.o. who loves it), a a failed query in Prolog implies the unknown state. It's about the provability within the system, not about a third truth value.

YeGoblynQueenne 3y ago
Yes, I see what you mean and it's a good observation and, funnily enough, you're both right and wrong. What you're saying is that Negation as Failure (NAF) introduces a concept of uncertainty, that we can consider a third truth value. Prolog doesn't have classical negation, where negating a logical atom (a "fact") makes it false, unconditionally and with certainty; it only has NAF, where an atom is true only if it cannot be disproved (since we prove by refutation). Intuitively speaking, that is right. NAF is the simplest way to treat uncertainty, or in any case there is no simpler way: just set aside what you cannot know with certainty, and proceed based on what you can (dis)prove with certainty. There's even a name for that: non-monotonic reasoning, and it's a powerful technique. There's an argument that's it's a good model of how humans reason about uncertainty. I'm agnostic on that front [1]. Formally speaking, thinking of Prolog as a ternary logic because of NAF is not right. NAF is just one way to assign truth values to atoms, but there are still only two truth values to assign, true or false. We might have uncertainty about the assignment, but that's still uncertainty about assignment of one of two values [2]. A bit more precisely, there are only two possible outcomes to a query: either it succeeds (one or more times, nondeterministically), or it fails. If the query succeeds we say that it was "true", for some values of the variables in the query, and if it fails we say it was "false", or there are no values of its variables that make it true. In other words, Prolog will never return a NULL, like SQL. The uncertainty is baked-in to the success or failure of a query. But that's a really cool subject and you are on the right track thinking of NAF in terms of uncertainty. __________________ [1] Answer Set Programming (ASP) is a different logic programming language where the difference between classical negation and NAF is part of the semantics of the language, and for the purpose of non-monotonic reasoning. I don't really know that literature very well so I can't recommend specific texts. [2] Also keep in mind that uncertainty exists only about the result of a query. Anything we declare as part of a Prolog program, "facts" and "rules", are axiomatically true. Since queries are proved by refutation that means that only falsehood is uncertain. We can know truth with certainty and un-truth with uncertainty.

by larodi 3y ago

YeGoblynQueenne 3y ago

Yes, I see what you mean and it's a good observation and, funnily enough, you're both right and wrong. What you're saying is that Negation as Failure (NAF) introduces a concept of uncertainty, that we can consider a third truth value. Prolog doesn't have classical negation, where negating a logical atom (a "fact") makes it false, unconditionally and with certainty; it only has NAF, where an atom is true only if it cannot be disproved (since we prove by refutation). Intuitively speaking, that is right. NAF is the simplest way to treat uncertainty, or in any case there is no simpler way: just set aside what you cannot know with certainty, and proceed based on what you can (dis)prove with certainty. There's even a name for that: non-monotonic reasoning, and it's a powerful technique. There's an argument that's it's a good model of how humans reason about uncertainty. I'm agnostic on that front [1]. Formally speaking, thinking of Prolog as a ternary logic because of NAF is not right. NAF is just one way to assign truth values to atoms, but there are still only two truth values to assign, true or false. We might have uncertainty about the assignment, but that's still uncertainty about assignment of one of two values [2]. A bit more precisely, there are only two possible outcomes to a query: either it succeeds (one or more times, nondeterministically), or it fails. If the query succeeds we say that it was "true", for some values of the variables in the query, and if it fails we say it was "false", or there are no values of its variables that make it true. In other words, Prolog will never return a NULL, like SQL. The uncertainty is baked-in to the success or failure of a query. But that's a really cool subject and you are on the right track thinking of NAF in terms of uncertainty. __________________ [1] Answer Set Programming (ASP) is a different logic programming language where the difference between classical negation and NAF is part of the semantics of the language, and for the purpose of non-monotonic reasoning. I don't really know that literature very well so I can't recommend specific texts. [2] Also keep in mind that uncertainty exists only about the result of a query. Anything we declare as part of a Prolog program, "facts" and "rules", are axiomatically true. Since queries are proved by refutation that means that only falsehood is uncertain. We can know truth with certainty and un-truth with uncertainty.