# Talk:Possibility theory

The article is fine and provides the potential readers with the necessary intuitive notions, definitions and motivations, as well as links to more specialised literature for specific topics.

Here are some comments or suggestions for improving several parts of the article:

1) Section Basic Notions

“unit interval” --> “real unit interval”

“flexible restriction on what the actual state is” ---> something like “flexible restriction on the set of states which are possible candidates for being the actual state”

About the query "does an event A occur?", this referee would add, for the sake of a better understanding "in the sense of 'is the actual state in A?' "

I do not think human knowledge is expressed by statements with attached belief degrees , if we think of degrees as numbers (for instance between 0 and 1). I would modify that sentence.

2) Section Qualitative possibility theory

In the first paragraph it is written "each prioritized formula has a fuzzy set of formulas (described earlier)", however I do not see where this is described, neither earlier nor later. I think the concepts described in this paragraph should deserve some more explanation.

I think that in this section something is missing about a very important form of qualitative knowledge, which is comparative knowledge. Actually, as far as I see it, prioritized formulas may be considered as a form of qualitative knowledge only if the scale used for weights is "qualitative in nature" enough. For instance, I would not say that a prioritized formula "(cloudy weather, 0.85)" is a qualitative expression, but I would accept it is so in the case of a formulas "((cloudy weather, likely)". However, comparative expressions, like "A is as possible as B", or under the more compact form of prioritized knowledge bases(as developed by the author, Benferhat and colleagues), with no explicit reference to weights, conform a much more qualitative setting, that I think should deserve some attention in this section.

3) Section Quantitative possibility theory

This section It seems it is too biased towards possible interpretation of possibility distributions in terms of other notions mostly related to probability theory. I miss in this section some references to developments of possibilistic graphical models or possibilistic belief networks and its inferential equivalence / relationship to possibilistic knowledge bases.

4) Section Applications

I miss in the article, here or in some other section, a brief description of the possibilistic framework for decision under uncertainty, a very interesting issue that deserves to be mentioned in opinion of this referee.

5) References

The reference De Campos - Huete has apparently extra page numbers

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Replies to referee. Many thanks for the remarks. We modified the article accordingly wherever we agreed.

“unit interval” --> “real unit interval”

A: Usually there is no ambiguity here. I put it explicitly.

“flexible restriction

A: This more complex sentence looks more difficult to understand.

"About the query "does an event A occur?",

"I do not think human knowledge is expressed by statements with attached belief degrees" A: OK modified.

Section Qualitative possibility theory

A: A first paragraph on comparative possibility is added. The semantics of possibilistic logic: the now second paragraph has been slightly expanded.

Section Quantitative possibility theory

A: I somewhat disagree. By "Quantitative possibility theory" we refer to the case where the unit interval is used with all its structure. We listed all interpretations of numerical possibility degrees we ever heard of.

The issue of possibilistic graphical models or possibilistic belief networks is another unrelated matter. We cite this issue at the end of the basic notion section.

"I miss in the article, here or in some other section, a brief description of the possibilistic framework for decision under uncertainty, "

A: A sentence is added where Dubois Prade Sabbadin is cited. But a full fledge presentation would take too long.