The FS-model is very simple and very easy to understand. The point of departure in possibility theory is the question: What is the possibility of p, with the understanding that possibility is a matter of degree, with degrees taking values in Concluding remark Let p be a proposition, possibly drawn from a natural language. Following is a brief synopsis of the theory. Extensive contributions to the development of possibility theory have been made by Dubois and Prade. In my 1978 paper on possibility theory, possibility theory is based on the theory of fuzzy sets.
![modal logic world diagrams modal logic world diagrams](https://i.imgur.com/Bv0NpJh.jpg)
State-transition function, f, s t + 1 = f ( s t, u t ) ,where s t is the state at time t, s t+1 Basics of possibility theory (2).Ī collection of collections of inputs, with each state, w i, associated with a collection of inputs, U i = ( u i1, …, u ik), with k dependent on w i, k = k( i). The states do have meaning in concrete versions of the FS-model. In the abstract model, the states are simply symbols with no meaning. W is referred to as the state space of FS. The FS-model has five principal components. It should be underscored that this note touches upon only elementary aspects of modal logic and possibility theory. A summary of the FS-model is described in the following. The FS-model is easy to understand and readily lends itself to generalization. , The FS-model may be viewed as a simple interpretation of Kripke model and is in the spirit of graph models of modal logic. There are many models which are equivalent to Kripke model. The best known model of modal logic is Kripke model. For comparison of modal logic with possibility theory, what is constructed in this note is a very simple abstract model which has the structure of a finite-state system, referred to as the FS-model. Modal logic is a deep theory which is not easy to understand. In large measure, what follows is motivated by the question: In what basic ways does the concept of possibility in modal logic differ from the concept of possibility in possibility theory? Interestingly, on a deeper level, a striking similarity comes to light. The role of the concept of possibility in modal logic is very different from its role in possibility theory. There are two theories in which the concept of possibility plays an important role-modal logic and possibility theory.