In terms of Artificial Intelligent and Logic Knowledge, What is the difference between sound and unsound reasoning?
Also, what kind of search Does ID3 algorithm use? Is it Breadth-first search?
Thanks
Question posted in Artificial Intelligence
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Answers
Reasoning is sound if the premises are true and the conclusion can be drawn from just those premises. For example:
is sound (ignoring other rep factors 🙂 ). If it read:
the reasoning would be valid, but not sound, because one of the premises is false
Two questions, not closely related. I answer only the first – do start a new SO question for the second.
There are two meanings of sound in logic. The first, which is prevalent in philosophy, is the one Michael gave. The second —which is generally used in formal logic, by logicians influenced by the terminology of model theory— is that sound inferences are truth-preserving, i.e., whenever the premises are true, so is the conclusion, or in other words, the premises imply the conclusion.
Note that the first is more demanding than the second: on the first account the premises of sound arguments need to be true, whilst on the second they do not. So all reasoning that is account-#1 sound are account-#2 sound, but not vice-versa, and Michael’s post explains why: the first of his examples is sound according to both criteria, whilst the second is sound only according to the second.
I think that in AI the second definition is more prevalent, but seeing as how AI is such a diverse discipline, with heavy influences from philosophy, you might well encounter the first. When I taught AI, I used the second.
I don’t know where the first definition came from, but the second is from Tarski. People who use the first definition of soundness use the term valid to talk about truth-preserving arguments. See the Internet Encyclopedia of Philosophy on Validity and Soundness for a discussion of the first definition, and Wikipedia’s article on Soundness for an explanation of the second.
A logic consists of a set of proposition and inference rules on these.
Given a logic L every proposition p that can be derived by the successive application of inference rules is said to be sound.
Any proposition p that cannot be derived can be said to be unsound, but no one says that. We just say that it is not in L.
A logic L is complete if every statement p that you (as an intelligent human) think should be true is sound.
Thus, we seek sound and complete logics.
This question sounds like a homework question for AI 101.