Possibility Theory
가능성 이론 (Possibility theory) 은 불확실성 (uncertainty) 을 다루는 수학이론이며 확률이론의 변형이라고 할수있다. Lofti A. Zadeh 가 그의 퍼지집합과 퍼지논리 이론의 확장으로서 1978 년에 가능성이론을 최초로 소개했다. 퍼지논리는 부정확성 (imprecision) 을 묘사하는 반면에 가능성이론은 불확실성 (uncertainty) 을 묘사한다. 이러한 생각이 완전히 새로운 것은 아니다. 1950 년대 경제학자 G.L.S. Shackle 은 degree of potential surprise 을 묘사하기 위해 min/max algebra 를 제안했었다. ......... (Wikipedia : Possibility theory)
가능성이론은 퍼지집합과 확률이론과 관련되어 있지만 독립적인 (independent) 새로운 형태의 정보이론이다. 기술적으로 가능성 분포 (possibility distributions) 은 일반적인 퍼지집합이다 (적어도 하나의 membership grade 는 1 과 같다). 예를들면, 모든 퍼지수 (fuzzy numbers) 는 가능성 분포이다. 그러나 가능성이론은 퍼지집합을 참조하지 않고도 유도될수 있다.
가능성이론의 규칙들은 확률이론과 유사하지만 확률의 PLUS/TIMES 논리 대신에 MAX/MIN or MAX/TIMES 논리를 사용한다. 또한 possibilistic NONSPECIFICITY 은 stochastic ENTROPY 와 유사한 정보의 측정으로서 이용될수 있다. 가능성이론은 시스템 속에서 nondeterminism 의 표현을 할때 확률이론보다 방법상의 장점을 가지고 있다. 왜냐하면 PLUS/TIMES 논리는 nondeterministic processes 를 일반화 하는데 유효하지 않지만 MAX/MIN and MAX/TIMES 은 유효하기 때문이다. .......... (source)
term :
퍼지 (Fuzzy) 퍼지 논리 (Fuzzy Logic) 확률 (Probability) 불확실성 (Uncertainty) Lofti A. Zadeh 양상논리 (Modal Logic) 가능성이론 (Possibility Theory)
site :
Wikipedia : Logical possibility
Philosophers generally consider logical possibility to be the broadest sort of subjunctive possibility in modal logic. The notion can be glossed by the popular description of logically possible propositions as those which can be asserted without any logical contradiction. Another way of saying this is that a proposition is logically possible if and only if there is some coherent way for the world to be, under which the proposition would be true. Thus, "the sky is blue" (and all other actually true propositions) is logically possible: there is a logically coherent way for the world to be under which it is true, such as the way that the world actually is. But this "way for the world to be" need not be the way the world actually is; it need only be logically coherent. So, for example, the false proposition the sky is green is also logically possible, so long as we are able (as we indeed seem to be) to conceive of some logically coherent world in which the sky is green.
These propositions, then, are to be contrasted with logically impossible propositions, i.e., propositions which could not possibly be true because they are formal contradictions. While it is logically possible for the sky to be green, it is not logically possible for the sky to be both green and not green at the same time and in the same respect. To conceive of the sky as green is to exclude it being non-green, and to conceive of it as non-green is to exclude it being green.
Logical possibility should be distinguished from other sorts of subjunctive possibilities. For example, it may be logically possible for the laws of nature to be different from what they actually are. The debate over whether it really is logically possible is beyond the scope of this article; the important thing to note here is that many philosophers have taken it for granted that it is logically possible; and if it is, then many things that we would normally consider to be demonstrably impossible will still be included amongst logical possibilities: for example, that I might fly by flapping my arms, or that I might throw a baseball faster than the 186,000 miles per second (300,000 km/s). Many philosophers, then, have held that these scenarios are logically possible but nomologically impossible, i.e., impossible under the actual laws of nature. Similarly, it's a perfectly genuine logical possibility that I might go on a senseless killing spree because I woke up on the wrong side of the bed one morning; but this is no accusation against my character, because while it's logically possible (there's no contradiction involved in supposing that it's true), it's not characterologically possible--there is no way that it could happen unless I cease to be the sort of person that I actually am.
With this understanding of logical possibility in mind, the other logical modalities may be defined in terms of it: a proposition is logically necessary if it is not logically possible for it to be false, logically impossible if it is not logically possible for it to be true, and logically contingent if it is logically possible for it to be true and also logically possible for it to be false.