Questions:

16. In denotational semantics, what are the syntactic and semantic domains?
17. What is stored in the state of a program for denotational semantics?
18. Which semantics approach is most widely known?
19. What two things must be defined for each language entity in order to construct a denotational description of the language?
20. Which part of an inference rule is the antecedent? 
21. What is a predicate transformer function?
22. What does partial correctness mean for a loop construct?
23. On what branch of mathematics is axiomatic semantics based?
24. On what branch of mathematics is denotational semantics based?

Answers:

16. The mapping functions of a denotational semantics programming language specification, like all functions in math, have a domain and a range, the domain is called the syntactic domain, and the range is called the semantic domain.
17. The state of a program for denotational semantics is the value of all its current variable.
18. The Denotational semantics is the most widely known semantics approach.
19. Objects and functions
20. The antecedent is the top part of an inference rule.
21. wp(statement, postcondition) = precondition
A wp function is often called a predicate transformer, because it takes a predi-
cate, or assertion, as a parameter and returns another predicate.
22. If loop termination can be shown, the axiomatic description
of the loop is called total correctness. If the other conditions can be met but
termination is not guaranteed, it is called partial correctness.
computing the precondition for a while loop depends on finding a loop invariant, proving the
correctness of programs with while loops using axiomatic semantics can be difficult.
23. Axiomatic semantics, thus named because it is based on mathematical logic.
24. mathematical objects (called denotations).