Page 79 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Unit 5: Artificial Intelligence Programming Language

Self Assessment Notes

State whether the following statements are true or false:
1. AI programming differs from standard software engineering approaches where
programming usually ends with a detailed formal specification.

2. A declarative programming style is more convenient using built-in high-level data
structures.
3. Lisp is not based on mathematical function theory and the lambda abstraction.

5.2 Predicates and Conditionals

Predicate logic builds heavily upon the ideas of proposition logic to provide a more powerful
system for expression and reasoning. As we have already mentioned, a predicate is just a function
with a range of two values, say false and true. We use predicates routinely in programming, e.g.
in conditional statements of the form
if(p(...args ...))

Here, we are using the two possibilities for the return value of p, (true or false). We also use the
propositional operators to combine predicates, such as in:
if(p(....) && (!q(....) || r(....)))
Predicate logic deals with the combination of predicates using the propositional operators we
have already studied. It also adds one more interesting element, the “quantifiers”. The meaning
of predicate logic expressions is suggested by the following:
Expression + Interpretation + Assignment = Truth Value

Now, we explain this equation.
An interpretation for a predicate logic expression consists of: a domain for each variable in the
expression a predicate for each predicate symbol in the expression a function for each function
symbol in the expression. Note that the propositional operators are not counted as function
symbols in the case of predicate logic, even though they represent functions. The reason for this
is that we do not wish to subject them to interpretations other than the usual propositional
interpretation. Also, we have already said that predicates are a type of function. However, we
distinguish them in predicate logic so as to separate predicates, which have truth values used by
propositional operators, from functions that operate on arbitrary domains.
Furthermore, as with proposition logic, the stand-alone convention applies with predicates. We
do not usually explicitly indicate == 1 when a predicate expression is true; rather we just write
the predicate along with its arguments, standing alone. An assignment for a predicate logic
expression consists of a value for each variable in the expression. Given an assignment, a truth
value is obtained for the entire expression in the natural way.

Example:
Consider the expression:
x < y || (y < z && z < x)
^ ^ ^ predicate symbols
Here || and && are propositional operators and < is a predicate symbol (in infix notation). An
assignment is a particular predicate, say the less_than predicate on natural numbers, and values
for x, y, and z, say 3, 1, and 2. With respect to this assignment then, the value is that of

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