The role of the notion of a proper answer in the logic of questions

The observations in the article mainly concern the role of the concept of the so-called right answer in question logic. The purpose of these remarks is to justify the postulate that any logic of questions should be based on a conception of the structure of questions and answers, in which the notion of a proper answer is strictly defined. This postulate is addressed to any question logic, although it is mainly supported and illustrated by analyses and comparative remarks referring to concepts based on Ajdukiewicz’s question theory and to recent approaches of inferential erotetic logic (IEL). The analyses confirm that the concept of proper answer is fundamental in question theories, as it is assumed in the definitions of almost all concepts relating to questions and answers. In Ajdukiewicz’s concept, it is used explicitly, for example, in the definitions of the conditions of proper questioning and of complete and exhaustive answers. In IEL, it appears explicitly in the definitions of: the pertinent question, the notion of the presupposition of a question (and its variations), the relations of evoking a question (by a set of indicative sentences) and implying a question (by another question), etc. This basic concept should therefore be well defined. This postulate applies especially to such theories of questions in which assertions about questions and answers are proved in symbolic language – as is the case in IEL, which, however, lacks a strict definition of the concept of proper answer (there are only vague, pragmatic terms formulated in natural language). There is, however, a definition that is closer to the idea of the proper answer, adopted by Ajdukiewicz as well as in the concepts related to it, that a proper answer is one the structure of which is determined by the scheme of the question structure. However, this definition should be complemented by an accurate and general conception of question structure, which is lacking in the existing concepts. In order to confirm the validity of the formulated postulate, the article proposes new results achieved in the theory of questions, in which Ajdukiewicz’s ideas are developed and supplemented by a full account of the structure of questions and well-defined, i.e. formulated in a general and strict way as is the idea of proper answer.

The Method of Socratic Proofs Meets Correspondence Analysis

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.

Questions

Some theorists hold that a question is an interrogative sentence; others that a question is what is meant or expressed by an interrogative sentence. Most theorists hold that each question has two or more answers, and that the point of asking a question is to have the respondent reply with one of the answers. Most hold that each question has an assertive core or presupposition that is implied by each of the answers; if it is false, then no answer is true, so we say that the question commits the fallacy of many questions and we regard the negation of the presupposition as a corrective reply to the question (it corrects the question). For example, consider the question ‘Has Adam stopped sinning?’ Its answers are ‘Adam has stopped sinning’ and ‘Adam has not stopped sinning’. It presupposes ‘Adam has sinned’; thus ‘Adam has not sinned’ is a corrective reply. The ‘safe’ way to ask this question is via the conditional ‘If Adam has sinned, then has Adam stopped sinning?’ We can construct formal systems for asking whether and which questions in an effective way. Other types of question (for example, who and why) are still problematic. It can be proved that some questions are reducible to others, some questions raise others, and some systems for the logic of questions can never be complete in certain ways.

Medical students’ vs. family physicians’ assessment of practical and logical values of pathophysiology multiple-choice questions

Testing strategies can either have a very positive or negative effect on the learning process. The aim of this study was to examine the degree of consistency in evaluating the practicality and logic of questions from a medical school pathophysiology test, between students and family medicine doctors. The study engaged 77 family medicine doctors and 51 students. Ten questions were taken from cardiac pathophysiology and 10 questions from pulmonary pathophysiology, and each question was assessed on the criteria of practicality and logic. A nonparametric Mann-Whitney test was used to test the difference between evaluators. On the criteria of logic, only four out of 20 items were evaluated differently by students in comparison to doctors, two items each from the fields of cardiology and pulmonology. On the criteria of practicality, for six of the 20 items there were statistically significant differences between the students and doctors, with three items each from cardiology and pulmonology. Based on these indicative results, students should be involved in the qualitative assessment of exam questions, which should be performed regularly under a strictly regulated process.

Foundations for the Logic of Questions and Commands

Recent interest in logics for questions and commands has been prompted partly by a recognition that reasoned argument often involves moves that are not truth-evaluable, and partly by the use of questions and commands in most procedural programming. The authors argue that certain methodological issues must be addressed before we can agree on the purpose and nature of logics for questions and commands. They deny that formulas in such logics should correspond to sentences in ordinary language. They consider how formulas should be interpreted, focusing especially on questions. The authors argue that logics designed to capture the conditions for correct reasoning involving questions require a semantics that treats question-answer pairs as values. This emphasis brings to the fore issues about questions in premise-conclusion arguments. In both premise-conclusion and dialogical argumentation, the authors argue that logic should aim to capture moves in reasoning, not facts about sentences.

Methodological Issues for the Logic of Questions and Commands

There has been much recent interest in logics for questions and commands. The authors approve, but they argue that methodological issues must be addressed, before it is possible to understand what such logics are for and what they should be like. In particular, the authors deny that the formulas in such logics correspond directly to sentences in ordinary language. Logic is not linguistics. What then are the semantics for the formulas of logics of questions and commands? The focus here is mostly on questions. The authors argue that logics designed to capture the conditions for correct reasoning involving questions require a semantics that treats question-answer pairs as values. They also argue that formal dialogue approaches to the logic of questions should be interpreted in the light of the denial that logic is about language.