Page 131 - Intelligent Communication Systems

I 1 0 INTELLIGENT COMMUNICATION SYSTEMS
Generally speaking, when A IS_A B, A is a concrete object and B is an abstract
concept that includes the concrete object A. In other words, B is a common concept
underlying object A. For example, the common concept underlying a Japanese, a
Chinese, and an American is a human. The common concept underlying a human
and an animal is a creature. When A PART_OF B, A is a component of B. For
example, a Japanese may be a component of a human. A Chinese is also a com-
ponent of a human.

iO.3 SYMBOLIC LOGIC

Predicate logic is used for telecommunication services such as intelligent direc-
tory service and intelligent switching service. In this section, predicate logic as well
as prepositional logic are described.
Mathematical logic includes predicate logic and prepositional logic. Each of
the following two sentences is a proposition, that is, a description of a specific
domain:
(1) The earth goes around the sun.
(2) A telephone is a terminal for telecommunication services.

Each proposition is composed of a primitive proposition or a compound
proposition, which is a combination of primitive propositions.
Every proposition is either true (T) or false (F). Proposition (1) and (2) are true.
On the other hand, the propositions "The earth is a triangle" and "A human is a
bird" are false.

10.3.1 Definition of a Proposition and Its Operations
A. proposition can be represented by a symbol, called an atomic formula, such as
p, q, r, and s. An atomic formula is either true (T) or false (F).
An operator that performs an operation on one or more atomic formulas is
called a logical symbol, for example, <-», ~, —», v, or A. The priority of operators
is as follows:
_
(1)
(2) A
(3) v
(4) -»
(5) <-»
where (1) is the highest priority and (5) is the lowest priority. The operators have
the following meanings:
"~" is a negation.
"A" is a conjunction.