"... In PAGE 11: ... Since all variables are Boolean, the relationship between y, x and v can be tabulated as in Table 1. In Table1 each assignment of values to v and x determines a possible way the vehicle/pedestrian encounter could have occurred. The rows of such tables have been variously referred to as quot;states of affairs, quot; quot;scenarios, quot; or quot;system states, quot; but a long-running practice in philosophical logic (e.... In PAGE 11: ... For example, suppose one is interested in whether or not the vehicle was speeding, but the only evidence is that the accident occurred (y=1). Table1 shows that the condition y=1 eliminates world 3 as a possibility, but of the remaining three worlds at least one has v=0 and one has v=1, so the best that can be said is that it is possible, but not necessary, that the vehicle was speeding. On the other hand, suppose that a reliable witness reported that the initial distance was quot;long quot; (x=1) when the pedestrian entered the road.... In PAGE 11: ... Uncertainty can be modeled by placing a probability distribution on the set of possible worlds, so that the probability attached to a statement is simply the probability assigned to the set of possible worlds where that statement is true. For example, suppose that each of the possible worlds in Table1 is regarded as a priori equally probable, so that each has a prior probability of 1/4. One then... In PAGE 12: ... For instance, suppose the actual world is world 4 (v=1, x=1) and world 3 (v=0, x=1) is taken to be the world closest to world 4, but having v=0. Letting yv=0=0 stand for the counterfactual claim that had v been 0, y would have been 0, Table1 shows that since y=0 is true in the possible world 3, yv=0=0 should be taken as true in the actual world 4. On the other hand, yv=0=0 should not be taken as true in world 2 (v=1, x=0) if world 1 (v=0,x=0) is taken as the closest with v=0.... ..."

"... In PAGE 6: ... There are many obvious connections between the logic-based and probability-based formalisms. For example, we can view the possible worlds (as shown in Table2 ) as a \qualitative quot; version of the atomic events (see Table 1), with the understanding that each \impossible quot; world has probability 0 of occuring, and the other possible words have non-0 probability. Many, including Nilsson [Nil86], have provided formalisms that attempt link these areas.... In PAGE 13: ... We can also consider stochastic algorithms here. One recent, prominent example is the GSAT algorithm [SLM92], which attempts to solve satis ability problems by hill-climbing and plateau- walking in the space of assignments, strarting from a random starting assignment (think \row of Table2 quot;). For example, the score of an assignment, for a xed 3SAT formula with m clauses, is the the number of clauses that are satis ed; note this score ranges from 0 to m.... ..."

"... In PAGE 5: ... Evidently, digital camera is an information entity whose contents and structure in this particular example vary according to the browsing device and the method of payment. In database terms there is a main relation dcamera, with attributes: Brand, Model, MPix, Photo, Price (see Table1 b). Customer requests are expressed as queries and the data returned correspond to the evaluation of the queries over this relation.... In PAGE 5: ... This is due to the fact that an attribute may not exist in some worlds and that the same attribute may have difierent values under difierent worlds. Table1 a presents all the possible worlds, while Table 1b... In PAGE 7: ... In order to show the basic parts of our model, we highlight the entity e4, the attribute Photo and the world w2. Entities belonging to context-relation dcamera have values for the six worlds of Table1 a. As stated in Table 1b, attribute Photo is not deflned for worlds w3 and w6 (device = CELL PHONE), it stores a high resolution photo for worlds w1 and w4 (device = PC) and a low resolution one for worlds w2 and w5 (device = PDA).... ..."

"... In PAGE 5: ... For example, suppose wehave a decision to continue smoking or quit, and we model the consequences of getting cancer or not. These acts and consequences bring to mind four possible states of the world, as shown in Table2 . These possible states haveno familiar names; and we simply label them with numbers.... In PAGE 5: ... For example, the state of the world may correspond to degree of susceptibility of lung tissue to tar as measured by a biochemical assay. Nonetheless, given the discrete acts and consequences that wehavechosen to model in the problem, the four states in Table2 are su#0Eciently detailed. Savage recognizes this issue of detail in his de#0Cnition of state of the world: #5Ca description of the world, leaving no relevant aspect undescribed.... ..."

"... In PAGE 5: ... For example, suppose wehave a decision to continue smoking or quit, and we model the consequences of getting cancer or not. These acts and consequences bring to mind four possible states of the world, as shown in Table2 . These possible states haveno familiar names; and we simply label them with numbers.... In PAGE 5: ... For example, the state of the world may correspond to degree of susceptibility of lung tissue to tar as measured by a biochemical assay. Nonetheless, given the discrete acts and consequences that wehavechosen to model in the problem, the four states in Table2 are sun0eciently detailed. Savage recognizes this issue of detail in his den0cnition of state of the world: n5ca description of the world, leaving no relevant aspect undescribed.... ..."

"... In PAGE 11: ... The rst two probabilities are given with the digraph. In this particular example it will be demonstrated that max P r(x3)= 3 max P r(x4)= 4 max P r(x5)= 5 and that min P r(x3) maxf0; 1 + 2 + 3 ? 2; 1 ? 5g min P r(x4) maxf0; 2 + 4 ? 1; 1 ? 5g min P r(x5) maxf0; 1 + 2 + 3 + 4 + 5 ? 4g Table2 shows the set of possible worlds and the associated probabilities for this example. The probabilities of the possible worlds are denoted by p1; p2; : : : ; p32.... ..."

"... In PAGE 6: ... Some movie sources sons, 4 possible worlds with 3 persons and 2 possible worlds with 2 persons. The possible worlds are summarized in Table1 . In this table each row represents a possible world and each column represents one person.... ..."

"... In PAGE 3: ...d as unclear responses. We return to this point below. To implement the situational models themselves two dif- ferent representational schemes were investigated, which we label probabilistic and reason-based . Table3 shows the set of candidate situational models which could be considered under each representational scheme. Each situational model is intended to represent a single possible state of the world (we refer to these as possible worlds , although the term is not used in its formal sense).... In PAGE 4: ... Supporting and opposing reasons provide qualitative but inconclusive evidence for or against the proposition, respec- tively. Table3 shows the candidate situational models which can be chosen from by the Build Model process using the reason-based representational scheme. This set of candidates Table 5: Proportion of compatible models produced for each stimulus under the probabilistic representational scheme.... ..."