Nuel D. Belnap and Thomas B. Steel (1976). The logic of questions and answers. Yale University Press.
What I will be looking for in the Belnap and Steel book is what their erotetic logic implies for the design of valid achievement test items, or any kind of question that might possibly be used to test a student for understanding something.
The first example makes it perfectly clear that this book might have impact on the way validity of test items might be assessed.
Belnap and Steel call this kind of question the 'Please relieve my vague puzzlement' kind of question, and they explicitely decline to treat it in their book. In a way, that's a pity. My and your hunch is that many questions put to students are of the 'Please relieve my vague puzzlement' kind. At least, students will have that impression, and that is what counts. Some teachers will sense trouble, and will write out what answers they will count as good answers, or which elements should be present in the answer in order to earn the student some points, etcetera. Of course, this attempt to objectify what is inherently vague, does not save this kind of question. The students still will not know what the assessors might have decided by fiat to count as good answers.
By default, test items leaving it unclear what will count as an answer, might be of the 'Please relieve my vague puzzlement' kind. What counts as an answer, therefore, is what counts. Belnap and Steel: "we want users of this logic to be able to calculate what counts as an answer to the questions we formalize. For this reason, the scope of our formalization is confined to the situation in which what counts as an answer to a given question is well defined in advance." What the authors intend to say here is that the question itself must allow the calculation of what will count as an answer. Any definition by fiat of what will count as an answer, however much used in educational testing, is ruled out.
Belnap and Steel restrict their logic to fairly elementary types of questions. The important class of why-questions is barely touched upon at all (a small paragraph in chapter 2, explaining why they will not be treated in this book). That is a severe omission, especially from the standpoint of the designer of achievement test items. If the designer opts for the theory that every achievement test item fundamentally is a why-question, asking for the explanation of given facts A and B, using theory T—the Hintikka (2007) approach, for example—then the Belnap and Steel logic of questions and answers might not be of any practical value at all. So, let us see what is the case.
An important observation on the domain of the Belnap and Steel book is that they—implicitly?—restrict their logical activities to questions of what I will call the Please inform me type: How many bones in a lion? Has John stopped beating his wife? Etcetera. These are not the kinds of questions that bother teachers, for they will want to know Does Mary know how many bones there are in a lion? Typically, teachers very well know the answers to their direct questions. The information they are seeking is whether the student knows or understands A, given B and a theory T. Therefore, they pose a concrete question asking for A, given B, supposing T. Or whatever. But, the real question, I will call it the intended question, is about mastery of the student. Every intended question makes use of at least one concrete question. The intended question, more often then not, is not made explicit, but is understood by all parties involved. The Belnap and Steel book is about the concrete questions. It probably is not conceivable to develop their kind of erotetic logic for intended questions as well. They are of a very, very complex kind.
The Belnap and Steel essay nevertheless is very useful because it elucidates many points about concrete questions, thus helping to better get to grips with the intended questions (I have used this insight in 'Toetsvragen ontwerpen' 2.6). Of course, validity issues of achievement test items necessarily will mostly be validity issues of their intended question forms. One of the lessons Belnap and Steel have taught me, is that some things implicit in questioning, the presuppositions etcetera, can be and should be made explicit in order to better understand the questioning and what will count as answers.
What will count as an answer to a concrete question might be fairly clear to all involved, what will count as an answer to an intended question is not immediately clear at all. There is a lot of work to do here, work that Belnap and Steel have not the need for?
Is John going home? (p.4)
Which positive integer is the smallest odd prime (p. 4)
Have you stopped beating your wife? (p. 5)
Who is that man living next door? (p. 11)
What is the relation between thought and language? (p. 12)
What is a number? (p. 12)
Why are there so many different kinds of atomic particles?
How do children learn language? (p. 12)
What is agood account of the question-answer situation? (p. 12)
(1) What is the freezing point of water, in degrees Hahrenheit, under standard conditions? (p. 3)
What is a good method of trisecting angles by means of ruler and compass? (p. 15)
What is a good method of trisecting angles by means of ruler and compass—or isn't there any? (p. 15)
Archimedes presents that method, using the ruler in a way that is not allowed in Euclid. b.w.
(2) Is glass a liquid at 70°F.? (p. 17)
Does brass contain more copper than tin or more tin than copper? (p. 18)
Which primes lie between 10 and 20? (p. 18)
What's an example of a prime lying between 10 and 20? (p. 18)
(4) Tobacco smoking: a vice, a virtue, a vagary, an extravagance, a cure for all ills?
(8) Has John stopped beating his wife? (p. 22)
(9) Which psitive integer is the smallest prime greater than 45?
(12) Which boys are brothers of which girls? (p. 24)
(15) What is the solution of a+x = b? (p. 25)
In what country is Lake Hjälmaren located? (p. 30) [Aqvist]
(20) What is the positive square root of π? (p. 31)
What is the positive square root of π, truncated after five decimal places? (p. 31)
(22) Which prime lies between 10 and 20? (p. 32)
Which theorems of the first order functional calculus contain exactly fourteen symbols? (p. 33)
What are the rational roots of x2 = 2? (p. 33)
What's an example of something not triangular? (p. 33)
(26) Which prime lies between 10 and 20? (p. 37)
(27) What's an example of a prime lying between 10 and 20? (p. 38)
(28) What are some of the primes lying between 10 and 20? (p. 38)
(29) Which primes lie between 10 and 20, or aren't there any? (p. 38)
(29') What are the freezing points of water, in degrees Hahrenheit, under standard conditions? (p. 40)
What are a few cities with populations greater than that of Boston? (p. 46)
(38) Did you say valor, or value? (p. 46)
Who are 5% of the secretaries listed? (p. 49)
(47) Which of lamb, beef, veal, and ham is on sale today? (p. 54)
(55) Which of the kitchen, the pantry and the wine cellar seems to you as likely a place as any to commence looking for the missing hat pin? (p. 58)
(56) Was her ladyship wearing the emerald necklace, the diamond bracelet, or both? (p. 58)
(57) Was it suicide or murder? (p. 58)
(58) What's at least one example of a truth among the following: the butler is concealing something, the upstairs maid knows more than she's telling, it would be worth questioning the gardener once again? (p. 59)
(59) Who were the denouncers of Cataline? (p. 60)
(63) What are at least five examples of primes? (p. 61)
(70) What are the square roots of 1/4? (p. 66)
(76) Which numbers are prime? (p. 73)
Nuel D. Belnap, Jr., and Thomas B. Steel, Jr. (1976). The logic of questions and answers. London: Yale University Press.
Dit boek behandelt exact wat de titel ervan belooft: een logisch filosofische verdieping voor de kunst van het vragenstellen. Bevat een rijke bibliografie, opgedeeld in 'Logic and philosophy of language', 'Linguistics', 'Automatic question answering', & 'Psychology and pedagogy'.
Zie ook het lemma Epistemic knowledge in de Stanford Encyclopedia of Philosophy html.
Debra Thomas Burhans (2002). A question answering interpretation of resolution refutation. A dissertation submitted to the Faculty of the Graduate School of State University of New York at Buffalo in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Een recente studie in de lijn van Belnap en Steel PostScript
Jaakko Hintikka (2007). Socratic epistemology. Explorations of knowledge-seeking by questioning. Cambridge University Press.