Defining answer classes using resolution refutation

Resolution theorem proving provides a useful paradigm for the exploration of question answering. A partition of the clauses generated during resolution refutation based on their syntactic structure is presented. The three classes comprising this partition correspond to semantically intuitive types of answers. This work encompasses and expands upon previous work on question answering in a theorem proving paradigm, which began with the association of answers with proofs. A complete, formal definition of what is meant by answer in the context of resolution theorem proving is presented. In this context, clauses that are relevant are all identified as answers, where relevance is determined with respect to a question and knowledge base: any clause descended from the clause form of a negated question is deemed relevant. This definition of relevance is not in and of itself novel; rather, it is the way in which the set of relevant clauses is partitioned that provides the key to interpreting clauses as answers. The three answer classes identified are: specific, generic, and hypothetical. These classes are formally distinguished by the way in which literals in a clause share variables, with class membership based on a property termed the closure of variable sharing of a literal. The results presented provide a foundation for further work by establishing a context-independent logical pragmatics of question answering.     

Locke and Hume on Belief, Judgment and Assent

Hume's account of belief has been much reviled, especially considered as an account of what it is to assent to or judge a proposition to be true. In fact, given that he thinks that thoughts about existence can be composed of a single idea, and that relations are just complex ideas, it might be wondered whether he has an account of judgment at all. Nonetheless, Hume was extremely proud of his account of belief, discussing it at length in the Abstract, and developing it in the Appendix. Furthermore, he claimed several times that his account was new. It was not just a new answer to an old question, but an answer to a new question as well. Why did Hume think he was raising, and answering, a new question? Is his answer really so appalling? Why did he define belief in terms of a relationship with a present impression? In this paper, I propose answers to these questions. The answers emerge by contrasting Hume with Locke. Locke thought that belief was a pale imitation of knowledge, and that the assent we give to propositions is constituted in the very same act as forming those propositions. Hume saw the problems such a theory faced concerning existential beliefs. By ceasing to treat existence as a predicate, Hume was confronted with the issue of what it was to judge something to be true, or to assent to something. This issue had to be solved independently of the question of what it was to conceive something, or understand the content of a proposition. Hume thought this problem was new. He should be looked at, not as giving a bad answer to an important question, but rather as being the first in the early modern period to recognize that there was an important question here to be answered.     

Double-Negation Elimination in Some Propositional Logics

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study.     

Why Care about Being an Agent?

The question ‘Why care about being an agent?’ asks for reasons to be something that appears to be non-optional. But perhaps it is closer to the question ‘Why be moral?’; or so I shall argue. Here the constitutivist answer—that we cannot help but have this aim—seems to be the best answer available. I suggest that, regardless of whether constitutivism is true, it is an incomplete answer. I argue that we should instead answer the question by looking at our evaluative commitments to the exercise of our other capacities for which being a full-blown agent is a necessary condition. Thus, the only kind of reason available is hypothetical rather than categorical. The status of this reason may seem to undermine the importance of this answer. I show, however, that it both achieves much of what we want when we cite categorical reasons and highlights why agency is valuable.     

On Moderate Pluralism About Truth and Logic

According to moderate truth pluralism, truth is both One and Many. There is a single truth property that applies across all truth-apt domains of discourse, but instances of this property are grounded in different ways. Propositions concerning medium-sized dry goods might be true in virtue of corresponding with reality while propositions pertaining to the law might be true in virtue of cohering with the body of law. Moderate truth pluralists must answer two questions concerning logic: (Q1) Which logic governs inferences concerning each truth-apt domain considered separately? (Q2) Which logic governs inferences that involve several truth-apt domains? This paper has three objectives. The first objective is to present and explain the moderate pluralist’s answers to (Q1) and (Q2). The second objective is to argue that there is a tension between these answers. The answer to (Q1) involves a commitment to a form of logical pluralism. However, reflection on the moderate truth pluralist’s answer to (Q2) shows that they are committed to taking logic to be topic neutrality. This, in turn, forces a commitment to logical monism. It would seem that the moderate truth pluralist cannot have it both ways. The third objective is constructive in nature. I offer an account of what moderate truth pluralists should say about logic and how they might resolve the tension in their view. I suggest that, just like moderate truth pluralists distinguish truth proper and “quasi-truth,” they should endorse a distinction between logic proper and “quasi-logic.” Quasi-truth is truth-like in the sense that instances of quasi-truth ground instances of truth. Quasi-logic is logic-like in the sense that it concerns arguments that are necessarily truth-preserving but are not generally so in a topic neutral way. I suggest that moderate truth pluralists should be monists about truth proper and logic proper but pluralists about quasi-truth and quasi-logic. This allows them to say that logic proper is topic neutral while still accommodating the idea that, for different domains, different arguments may be necessarily truth-preserving.     

Regulation of memory accuracy with multiple answers: the plurality option

We report two experiments that investigated the regulation of memory accuracy with a new regulatory mechanism: the plurality option. This mechanism is closely related to the grain-size option but involves control over the number of alternatives contained in an answer rather than the quantitative boundaries of a single answer. Participants were presented with a slideshow depicting a robbery (Experiment 1) or a murder (Experiment 2), and their memory was tested with five-alternative multiple-choice questions. For each question, participants were asked to generate two answers: a single answer consisting of one alternative and a plural answer consisting of the single answer and two other alternatives. Each answer was rated for confidence (Experiment 1) or for the likelihood of being correct (Experiment 2), and one of the answers was selected for reporting. Results showed that participants used the plurality option to regulate accuracy, selecting single answers when their accuracy and confidence were high, but opting for plural answers when they were low. Although accuracy was higher for selected plural than for selected single answers, the opposite pattern was evident for confidence or likelihood ratings. This dissociation between confidence and accuracy for selected answers was the result of marked overconfidence in single answers coupled with underconfidence in plural answers. We hypothesize that these results can be attributed to overly dichotomous metacognitive beliefs about personal knowledge states that cause subjective confidence to be extreme.     

On Liking Aesthetic Value

According to tradition, aesthetic value is non-contingently connected to a certain feeling of liking or pleasure. Is that true? Two answers are on offer in the field of aesthetics today: 1. The Hedonist answers: Yes, aesthetic value is non-contingently connected to pleasure insofar as this value is constituted and explained by the power of its possessors to please (under standard conditions). 2. The Non-Affectivist answers: No. At best, pleasure is contingently related to aesthetic value. The aim of this paper is to point to a blind spot in the dialectic between these two standard positions by defending a third neglected answer to the question above, the answer of the Value-Meriting-Pleasure [VMP] advocate. According to this answer, a certain kind of (cognitive and responsive) pleasure is connected to aesthetic value non-contingently, but also non-hedonically. VMP is the view that objects of aesthetic value are non-contingently related to pleasure insofar as they merit a certain kind of pleasure. But, pace the hedonist, those objects are valuable (those that are to be engaged with etc.) neither on account of their capacity to give pleasure nor on account of the hedonic value of the attitude they merit.     

The Existential Quantifier, Composition and Contingency

There is a good deal of disagreement about composition. There is first-order disagreement: there are radically different answers to the special composition question—the question of under what circumstances the xs compose a y. There is second-order disagreement: there are different answers to the question of whether first-order disagreement is real or merely semantic. Virtually all disputants with respect to both the first- and second-order issues agree that the answer or answers to the special composition question will take the form of a necessary truth or truths even though, as I will argue, such answers do not appear to be good candidates to be necessary truths. This paper provides an analysis of the concept of <exists> as it pertains to concrete objects, that fulfils two functions. First, it explicates the sense in which claims about composition are contingent and the sense in which they are necessary, and second, it provides a way of understanding when first-order disputes are substantial and when they are merely semantic.     

Reliability and the Value of Knowledge*

Reliabilism has come under recent attack for its alleged inability to account for the value we typically ascribe to knowledge. It is charged that a reliably‐produced true belief has no more value than does the true belief alone. I reply to these charges on behalf of reliabilism; not because I think reliabilism is the correct theory of knowledge, but rather because being reliably‐produced does add value of a sort to true beliefs. The added value stems from the fact that a reliably‐held belief is non‐accidental in a particular way. While it is widely acknowledged that accidentally true beliefs cannot count as knowledge, it is rarely questioned why this should be so. An answer to this question emerges from the discussion of the value of reliability; an answer that holds interesting implications for the value and nature of knowledge.     

Using the regulation of accuracy to study performance when the correct answer is not known

We examined memory performance in multiple‐choice questions when correct answers were not always present. How do participants answer when they are aware that the correct alternative may not be present? To answer this question we allowed participants to decide on the number of alternatives in their final answer (the plurality option), and whether they wanted to report or withhold their answer (report option). We also studied the memory benefits when both the plurality and the report options were available. In two experiments participants watched a crime and then answered questions with five alternatives. Half of the questions were presented with the correct alternative and half were not. Participants selected one alternative and rated confidence, then selected three alternatives and again rated confidence, and finally indicated whether they preferred the answer with one or with three alternatives (plurality option). Lastly, they decided whether to report or withhold the answer (report option). Results showed that participants’ confidence in their selections was higher, that they chose more single answers, and that they preferred to report more often when the correct alternative was presented. We also attempted to classify a posteriori questions as either presented with or without the correct alternative from participants’ selection. Classification was better than chance, and encouraging, but the forensic application of the classification technique is still limited since there was a large percentage of responses that were incorrectly classified. Our results also showed that the memory benefits of both plurality and report options overlap.     

Dialogue representation

We consider question-answer dialogues between participants who may disagree with each other. The main problems are: (a) How different speech-acts affect the information in the dialogue; and (b) How to represent what was said in a dialogue, so that we can summarize it even when it involves disagreements (i.e., inconsistencies).We use a fully-typed many-sorted language L with a possible-worlds semantics. L contains nominals representing short answers. The speech-acts are uniformly represented in a dialogue language DL by focus structures, consisting of a mood operator, a topic component and a focus component. Each stage of the dialogue is associated with a set of information functions (g-functions), which are partial functions taking a topic component (representing a question raised) to a set of propositions determined by the corresponding focus component (to the set of answers given to it).Asserting is answering a question and, hence, it causes a new g-function to be defined. Asking is an attempt to cause the hearer to define a new g-function satisfying certain conditions. A question asked requests a true and complete answer. A reaction answers a question if it satisfies some of the conditions of the question. Indirect questions are viewed as indirect answers.A dialogue representation consists of: commitment sets, each representing the commitments expressed by one participant; sets of questions under discussion associated with each stage of the dialogue, and the common ground, containing the g-functions and representing consistently what was said in the dialogue.Concepts of informativeness are naturally defined within the theory. Whether an utterance is informative depends on which question it answers and how the question was answered previously. These concepts yield that uttering mathematical and logical truths is as informative as uttering a contingency.     

Different answers to different audiences: effects of social context on the accuracy-informativeness trade-off

Research on conversational exchanges shows that people attempt to optimise their responses’ relevance when they definitely know the correct answer (e.g., “What time is it?”). However, such certainty is often unavailable while speakers may still be under social pressure to provide an answer. We investigated how social context influences the informativeness level when answering questions under uncertainty. In three experiments, participants answered difficult general-knowledge questions placed in different social contexts (formal vs. informal). Participants generated their answers, then they were presented with a given context, and decided on the number of alternative responses they wanted to provide (single, with one alternative vs. plural, with several alternatives) and whether the answer should be reported or withheld (report option). Participants reported more answers in the informal context. In the formal context, single answers were preferred, and they were more frequently reported. We conclude that social context influences the level of informativeness in a conversation, affecting achievable accuracy. Our results also show the joint influence of the confidence and the social context on willingness to share information.     

Data-driven type checking in open domain question answering

Many open domain question answering systems answer questions by first harvesting a large number of candidate answers, and then picking the most promising one from the list. One criterion for this answer selection is type checking: deciding whether the candidate answer is of the semantic type expected by the question. We define a general strategy for building redundancy-based type checkers, built around the notions of comparison set and scoring method, where the former provide a set of potential answer types and the latter are meant to capture the relation between a candidate answer and an answer type. Our focus is on scoring methods. We discuss nine such methods, provide a detailed experimental comparison and analysis of these methods, and find that the best performing scoring method performs at the same level as knowledge-intensive methods, although our experiments do not reveal a clear-cut answer on the question whether any of the scoring methods we consider should be preferred over the others.     

Coordinating mathematical concepts with the demands of authority: children’s reasoning about conventional and second-order logical rules

Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect answers. Hence these rules are not legitimately alterable by authority. Second-order logical rules depend on the particular conventions of the symbol system used (e.g. the rule for carrying in place-value addition). Given the symbol system used, these rules are not legitimately alterable by authority. However, as a result of their dependence on the symbol system, children may have difficulty distinguishing second-order logical rules from conventional rules. Ninety-eight children in grades 2 through 5 were interviewed about the correctness of answers obtained using alternatives to standard conventional and second-order logical rules, and about the legitimacy of authorities to change the rules. Half the children across this age range treated second-order logical rules as somewhat like conventions, judging that an answer resulting from an alternative to a second-order logical rule is correct if sanctioned by authority. With increasing age children increasingly limited the jurisdiction of authority over second-order logical rules.     

Insensitivity and oversensitivity to answer diagnosticity in hypothesis testing

Two experiments examined how people perceive the diagnosticity of different answers (“yes” and “no”) to the same question. We manipulated whether the “yes” and the “no” answers conveyed the same amount of information or not, as well as the presentation format of the probabilities of the features inquired about. In Experiment 1, participants were presented with only the percentages of occurrence of the features, which most straightforwardly apply to the diagnosticity of “yes” answers. In Experiment 2, participants received in addition the percentages of the absence of features, which serve to assess the diagnosticity of “no” answers. Consistent with previous studies, we found that participants underestimated the difference in the diagnosticity conveyed by different answers to the same question. However, participants' insensitivity was greater when the normative (Bayesian) diagnosticity of the “no” answer was higher than that of the “yes” answer. We also found oversensitivity to answer diagnosticity, whereby participants valued as differentially diagnostic two answers that were normatively equal in terms of their diagnosticity. Presenting to participants the percentages of occurrence of the features inquired about together with their complements increased their sensitivity to the diagnosticity of answers. We discuss the implications of these findings for confirmation bias in hypothesis testing.     

“WHY BE MORAL?” The Cheng Brothers' Neo‐Confucian Answer

In this article, I present a neo‐Confucian answer, by Cheng Hao and Cheng Yi, to the question, “Why should I be moral?” I argue that this answer is better than some representative answers in the Western philosophical tradition. According to the Chengs, one should be moral because it is a joy to perform moral actions. Sometimes one finds it a pain, instead of a joy, to perform moral actions only because one lacks the necessary genuine moral knowledge—knowledge that is accessible to every common person as long as one makes the effort to learn. One should make the effort to learn such knowledge—to seek joy in performing moral actions—because to be moral is a distinguishing mark of being human. This neo‐Confucian answer seems to be egoistic, as its conception of motivation for morality is based on self‐interest: to seek one's own joy. However, since it emphasizes that one's true self‐interest is to seek joy in things uniquely human, which is to be moral, self‐interest and morality become identical; the more a person seeks one's self‐interest, the more moral the person is, and vice versa.     

Why it doesn’t matter whether the virtues are truth-conducive

A potential explanation of a fact is a hypothesis such that, if it were true, it would explain the fact in question. Let’s suppose that we become aware of a fact and some potential explanations thereof. Let’s also suppose that we would like to believe the truth. Given this aim, we can ask two questions. First, is it likely that one of these hypotheses is true? Second, given an affirmative answer to the first question, which one is it likely to be? Inference to the best explanation (IBE) offers answers to both questions. To the first, it says ‘Yes’—assuming that at least one of the hypotheses would, if true, provide a satisfactory explanation of the fact under consideration. To the second, it says that the hypothesis most likely to be true is the one that scores best on the explanatory virtues: conservatism, modesty, simplicity, generality, and predictive power. Many philosophers have argued against IBE’s answer to the first question. I am interested in an objection to its answer to the second. Many philosophers seem to think that it is unsustainable: they seem to think that even if we assume that one of the competing hypotheses is true, we should not think that IBE will help us to identify it. Or, more carefully, if these philosophers are doing what they appear to be doing—namely, offering critiques of IBE that don’t depend on assumptions about the field of competing hypotheses—then their claim is that IBE will not help us to identify the truth. I believe that this is mistaken: the argument for believing it assumes a model of IBE that we have no reason to accept.     

The artful dodger: answering the wrong question the right way

What happens when speakers try to "dodge" a question they would rather not answer by answering a different question? In 4 studies, we show that listeners can fail to detect dodges when speakers answer similar-but objectively incorrect-questions (the "artful dodge"), a detection failure that goes hand-in-hand with a failure to rate dodgers more negatively. We propose that dodges go undetected because listeners' attention is not usually directed toward a goal of dodge detection (i.e., Is this person answering the question?) but rather toward a goal of social evaluation (i.e., Do I like this person?). Listeners were not blind to all dodge attempts, however. Dodge detection increased when listeners' attention was diverted from social goals toward determining the relevance of the speaker's answers (Study 1), when speakers answered a question egregiously dissimilar to the one asked (Study 2), and when listeners' attention was directed to the question asked by keeping it visible during speakers' answers (Study 4). We also examined the interpersonal consequences of dodge attempts: When listeners were guided to detect dodges, they rated speakers more negatively (Study 2), and listeners rated speakers who answered a similar question in a fluent manner more positively than speakers who answered the actual question but disfluently (Study 3). These results add to the literatures on both Gricean conversational norms and goal-directed attention. We discuss the practical implications of our findings in the contexts of interpersonal communication and public debates.     

Relating familiarity-based recognition and the tip-of-the-tongue phenomenon: Detecting a word’s recency in the absence of access to the word

After viewing a list of single-word answers to general knowledge questions, participants received a test list containing general knowledge questions, some of whose answers were studied, and some of whose were not. Regardless of whether participants could provide the answer to a test question, they rated the likelihood that the answer had been studied. Across three experiments,participants consistently gave higher ratings to unanswerable questions whose answers were studied than to those whose answers were not studied. This discrimination ability persisted in the absence of reported tip-of-the-tongue (TOT) states and when no information about the answer could be articulated. Studying a question's answer did not increase the likelihood of a later TOT state for that question, yet participants gave higher recognition ratings when in a TOT state than when not in a TOT state. A possible theoretical mechanism for the present pattern is discussed, as are relevant theories of familiarity-based recognition and of the TOT phenomenon.     

The effect of question repetition within interviews on young children's eyewitness recall

This study investigated the influence of question repetition and question type (answerable, unanswerable, or opinion seeking) on children's recall. A total of 136 children (5-, 7-, and 9-year-olds) watched a live 15-min presentation. One week later, the children were asked 20 questions that were repeated an additional two times within the interview. Accuracy of children's responses to unanswerable questions declined with repetition. Children were more likely to change a response to an unanswerable question than to an answerable question. Overall, children maintained the same answers to only three-quarters of the repeated questions. The most common pattern of change was for children to change their answer the second time a question was asked and then to maintain that answer when questioned again. The high percentage of changed answers within a single interview has important implications for forensic interviewing.