Zeroth-Order Logic

Question 1

Another name for zeroth-order logic?

Answer 1

Propositional calculus; propositional logic; sentential calculus; sentential logic

Question 2

What distinguishes zeroth-order logics from higher-order logics?

Answer 2

Zeroth-order logic has an absence of variables and quantifiers

Question 3

Propositional calculus is a formal language L where L = ?

Answer 3

L = L(A, Ω, Ζ, Ι)

Question 4

The Alpha set (A) of formal language L contains ?

Answer 4

Finite set of propositional symbols, typically letters p, q, r

Question 5

The Omega set (Ω) of formal language L contains?

Answer 5

Finite set of operator symbols or logical connectives, such as ‘v’ and ‘–>’

Is partitioned into disjoint subsets:

Ω=Ω(0)UΩ(1)UΩ(2)U…UΩ(j)U…UΩ(m)

where 0, 1, 2, j, m are the arities of the subsets

Question 6

What is arity?

Answer 6

(of a function) the number of arguments or operands that a function takes

e.g.,

Ω(0)={0,1}
Ω(1)={~}
Ω(2)={v, &, –>, }

Question 7

The Zeta set (Z) of formal language L contains?

Answer 7

Finite set of transformation rules that are called inference rules when they take on logical applications

Question 8

The Iota set (I) of formal language L contains?

Answer 8

Finite set of initial points that are called axioms when they receive logical interpretations

Question 9

What are the three classical laws of thought?

Answer 9

law of identity; law of non-contradiction; law of excluded middle

Question 10

What is the law of identity?

Answer 10

Whatever is, is.

or,

for all a: a=a

Question 11

What is the law of non-contradiction?

Answer 11

Nothing can both be and not be.

or,

~(a&~a)

Question 12

What is the law of excluded middle?

Answer 12

Everything must either be or not be.

or,

av~a