Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

11.9 Conclusions
The chapter demonstrated the scope of the extension of the predicate logic
formalisms for reasoning with time and space. The principles of spatial
reasoning have been covered with FOL and fuzzy logic, whereas the temporal
reasoning is introduced with situation calculus and propositional temporal
logic. These are active research fields and we have to wait a few more years
for its complete formalization. Most important applications of spatio-temporal
reasoning include co-ordination and task planning of multiple robots for
handling a complex problem like machine repairing, where active
participation of a number of robots is required to share time and space. It
may be added here that some aspects of the co-ordination problems could
have been solved with timed Petri nets. We, however, will introduce timed
Petri nets and their application in co-ordination problems in chapter 24.
Another interesting topic, which we could not discuss here for lack of space,
is reasoning with shape [6]. This is important because, in any practical path
planning problems of mobile robots, knowing the 2-D and the 3-D shapes of
obstacles are useful for decision making. This also is an active area of
research and will require a few more years to take final shape.
Exercises
1. Write a logic program to describe the spatial relationships among the
components of a 4 legged table, assuming that at least three legs are
visible in the image.
2. Justify the definitions of µright (θ) by taking θ = -90 0 , 0 0 , 45 0 and 90 0 .
Can you define it in an alternative manner?
3. Graphically compute the membership of a triangle below a rectangle
following the method presented in the text. Also plot the f (θ).
4. Identify the events, fluents and the situations from the following
sentences: a) The teacher called John, the student, to the board. b) He
then handed over the chalk to John. c) He insisted John write what he
was talking to his classmates. d) Then he asked John to write what he was
teaching. e) John could not write anything but started trembling. f) The
teacher then advised John to leave the classroom.
5. Add the following rule to the previous facts and then show by situation
calculus that ‘the teacher advised John to leave the classroom’ directly
follows from the other facts.