Examples of computation/deduction

The following relatively simple examples are intended to illustrate application of deduction rules.

The Robert example

p: Usually, Robert returns from work at about 6:00 p.m. What is the probability that Robert is home at about 6.15 p.m.?

First, we find the protoforms of the information set and the query.

Usually, Robert returns from work at about 6:00 pm.-?

-? Prob(Time(Return(Robert)) is *6:00 pm.) is usually B/usually,

which in annotated form reads

-? Prob(X/Time(Return(Robert)) is A/*6:00 pm.) is B/usually,

where *a is an abbreviation of about a.

Likewise, for the query, we have Prob(Time(Return(Robert)) is =s o*6:15 p.m.) is ? D which in annotated form reads

-? Prob(X/Time(Return(Robert)) is C/^o *6:15 pm.) is D/usually,

where o is the operation of composition (Pedrycz and Gomide, 1998). Searching the computation/deduction module, we find that the basic probability rule matches the protoforms of the data and the query

where subject to

and r is the probability density of X.

Instantiating A, B, C and D, we obtain the answer to the query: Probability that Robert is home at about 6:15 pm. is D, where

subject to and