Homework 3

Due October 24, 2000

1. p. 147: Problem 5.8.a

2. pp. 180-181:

a) Problems 6.3.a, c, e, g.

b) Problem 6.4.

c) Problems 6.7.a, c.

d) Problem 6.8.b.

3. pp. 213-215:

a) Problems 7.2.a, b, d, i.

b) Problem 7.7.

4. Briefly define the following terms:

a) An interpretation in prepositional logic (PL)

b) Logical consequences

c) A sound inference rule

5. Short questions:

a) Show that inference rules “modus ponens”, “modus tollens”, and “chaining” can all be replaced by a single rule of resolution.

b) Predicates in first order logic (FOL) are special functions. Like other functions, a predicate is a function of terms (i.e., it takes terms as its arguments). However, predicates behavior differently than other functions. Give two major differences between predicates and other functions.