Negation: A theory of its meaning, representation, and use

Reasoning About Want

No present theory explains the inferences people draw about the real world when reasoning about "bouletic" relations, that is, predicates that express desires, such as want in "Lee wants to be in love". Linguistic accounts of want define it in terms of a relation to a desirer's beliefs, and how its complement is deemed desirable. In contrast, we describe a new model-based theory that posits that by default, desire predicates such as want contrast desires against facts. In particular, A wants P implies by default that P is not the case, because you cannot want what is already true. On further deliberation, reasoners may infer that A believes, but does not know for certain, that P is not the case. The theory makes several empirical predictions about how people interpret, assess the consistency of, and draw conclusions from desire predicates like want. Seven experiments tested and validated the theory's central predictions. We assess the theory in light of recent proposals of desire predicates.

"Looking at" Negation: Faster Processing for Symbolic Rather Than Iconic Representations

Many studies have shown the double processing of negation, suggesting that negation integration into sentence meaning is delayed. This contrasts with some researches that have found that such integration is rather immediate. The present study contributes to this debate. Affirmative and negative compound sentences (e.g., "because he was not hungry, he did not order a salad") were presented orally in a visual world paradigm while four printed words were on the screen: salad, no salad, soup, and no soup. The eye-tracking data showed two different fixation patterns for negative causal assertions, which are linked to differences in the representation and inferential demands. One indicates that negation is integrated immediately, as people look at the explicit negation (e.g., no salad) very early. The other, in which people look at the alternate (e.g., soup) much later, indicates that what is delayed in time is the representation of the alternate. These results support theories that combine iconic and symbolic representations, such as the model theory.

Inferences from the negation of counterfactual and semifactual conditionals

Our goal was to study how people understand the negation of counterfactuals (such as “Antonio denied/said that it is false that if Messi had played, then Barcelona would have won”) and semifactuals (such as “Antonio denied that even if Messi had played, Barcelona would have won”). Previous studies have shown that participants negated basic conditionals using small-scope interpretations by endorsing a new conditional with the negated consequent, but also by making large-scope interpretations, endorsing a conjunction with the negated consequent. Three experiments showed that when participants were asked whether the negation of a counterfactual (Experiments 1 and 2) or semifactual (Experiment 3) conditional was followed by a new conditional, they made a small-scope interpretation, endorsing the same conditional with the negated consequent (e.g., “if/even if Messi had played, Barcelona would not have won”). However, they also accepted the conditional with the negated antecedent for semifactuals (e.g., “even if Messi had not played, Barcelona would have won”). When participants were asked whether the negation of a counterfactual or semifactual conditional is followed by a conjunction, they endorsed the conjunction with both the negated antecedent and the consequent (e.g., “Messi did not play and Barcelona did not win”), but again they accepted the conjunction with the negated antecedent only for semifactuals (e.g., “Messi did not play and Barcelona did win”). These results have implications for the main theories of reasoning.

Alternatives or syntactic negation? Adults’ and children’s preferences for constructing counterfactual possibilities

Reasoning with counterfactuals such as “if his sister had entered silently, the child would have been awake”, requires considering what is conjectured (“his sister entered silently”) and what is the counterfactual possibility (“his sister did not enter silently”). In two experiments, we test how both adults (Study 1) and children from 8 to 12 years (Study 2) construct counterfactual possibilities about the cause of an effect (“the child was awake because…”). We test specifically whether people construct the counterfactual possibility by recovering alternatives, for example, “the alarm clock sounded” or by using the syntactic negation using propositional symbols (“his sister did not enter silently”). Moreover, as children show difficulty in thinking with abstract contents, we test whether they construct the counterfactual possibility more readily by recovering concrete alternatives (“the alarm clock sounded”) rather than abstract alternatives (“he had trouble sleeping”). Results showed that children, as well as adults, recovered the alternative as the cause of the effect rather than the negation. Moreover, children, unlike adults, created the counterfactual possibility more frequently by recovering concrete situations rather than abstract situations.

Similarities and differences in understanding negative and affirmative counterfactuals and causal assertions: Evidence from eye-tracking

Two eye-tracking experiments compared affirmative and negative counterfactuals, "if she had (not) arrived early, she would (not) have bought roses" and affirmative and negative causal assertions, "Because she arrived (did not arrive) early, she bought (did not buy) roses." When participants heard a counterfactual, they looked on screen at words corresponding to its conjecture ("roses"), and its presupposed facts ("no roses"), whereas for a causal assertion, they looked only at words corresponding to the facts. For counterfactuals, they looked at the conjecture first, and later the presupposed facts, and at the latter more than the former. The effect was more pronounced for negative counterfactuals than affirmative ones because the negative counterfactual's presupposed facts identify a specific item ("she bought roses"), whereas the affirmative counterfactual's presupposed facts do not ("she did not buy roses"). Hence, when participants were given a binary context, "she did not know whether to buy roses or carnations," they looked primarily at the presupposed facts for both sorts of counterfactuals. We discuss the implications for theories of negation, the dual meaning of counterfactuals, and their relation to causal assertions.

Much Ado About Nothing: The Mental Representation of Omissive Relations

When the absence of an event causes some outcome, it is an instance of omissive causation. For instance, not eating lunch may cause you to be hungry. Recent psychological proposals concur that the mind represents causal relations, including omissive causal relations, through mental simulation, but they disagree on the form of that simulation. One theory states that people represent omissive causes as force vectors; another states that omissions are representations of contrasting counterfactual simulations; a third argues that people think about omissions by representing sets of iconic possibilities – mental models – in a piecemeal fashion. In this paper, we tease apart the empirical predictions of the three theories and describe experiments that run counter to two of them. Experiments 1 and 2 show that reasoners can infer temporal relations from omissive causes – a pattern that contravenes the force theory. Experiment 3 asked participants to list the possibilities consistent with an omissive cause – it found that they tended to list particular privileged possibilities first, most often, and faster than alternative possibilities. The pattern is consistent with the model theory, but inconsistent with the contrast hypothesis. We marshal the evidence and explain why it helps to solve a long-standing debate about how the mind represents omissions.

The relative difficulty of negations of conjunctions and disjunctions-a mental model perspective

A current issue in propositional reasoning is which of negated disjunctions and conjunctions are more difficult to understand. Using the possibility generation and evaluation tasks, we investigated how people make possibility inferences from negated compound assertions such as not (A and B) and not (A or B). We derive 4 different strategies of negation from the mental model theory (the enumerative negation, the eliminative negation, the element negation, and the clause negation) to predict the relative difficulty of possibility inference from not (A and B) and not (A or B). The results of three experiments convergently demonstrate that possibility inference from not (A or B) is harder than that from not (A and B). Moreover, an interpretation of negation as the complement of the set of possibilities allowed by a compound assertion is in line with the results of not (A and B) rather than not (A or B). The overall results favor the clause negation strategy over the other strategies.

Explanatory completeness

All explanations are incomplete, but reasoners think some explanations are more complete than others. To explain this behavior, we propose a novel theory of how people assess explanatory incompleteness. The account assumes that reasoners represent explanations as causal mental models - iconic representations of possible arrangements of causes and effects. A complete explanation refers to a single integrated model, whereas an incomplete explanation refers to multiple models. The theory predicts that if there exists an unspecified causal relation - a gap - anywhere within an explanation, reasoners must maintain multiple models to handle the gap. They should treat such explanations as less complete than those without a gap. Four experiments provided participants with causal descriptions, some of which yield one explanatory model, e.g., A causes B and B causes C, and some of which demand multiple models, e.g., A causes X and B causes C. Participants across the studies preferred one-model descriptions to multiple-model ones on tasks that implicitly and explicitly required them to assess explanatory completeness. The studies corroborate the theory. They are the first to reveal the mental processes that underlie the assessment of explanatory completeness. We conclude by reviewing the theory in light of extant accounts of causal reasoning.

Reasoning about Durations

A set of assertions is consistent provided they can all be true at the same time. Naive individuals could prove consistency using the formal rules of a logical calculus, but it calls for them to fail to prove the negation of one assertion from the remainder in the set. An alternative procedure is for them to use an intuitive system (System 1) to construct a mental model of all the assertions. The task should be easy in this case. However, some sets of consistent assertions have no intuitive models and call for a deliberative system (System 2) to construct an alternative model. Formal rules and mental models therefore make different predictions. We report three experiments that tested their respective merits. The participants assessed the consistency of temporal descriptions based on statements using "during" and "before." They were more accurate for consistent problems with intuitive models than for those that called for deliberative models. There was no robust difference in accuracy between consistent and inconsistent problems. The results therefore corroborated the model theory.

Negation interacts with motivational direction in understanding action sentences

Linguistic negation acts by inhibiting the representation of information under its scope, often leading to the representation of positive alternative states of affairs. Motivational direction refers to approach/avoidance intentionality in our interactions with environmental stimuli expressed by means of verbs (e.g., “accept” vs “reject”). We consider it plausible that negation interacts with direction to represent the true motivation of the protagonist in sentence understanding (e.g., if an approach action is negated it is represented as avoidance). In the first study, we examine this interaction offline by asking participants to judge approach or avoidance meaning of affirmative (e.g., “he/she included/excluded meat”) and negative sentences (“he/she did not include/exclude meat”). Results support that negation reversed participants’ interpretation of sentence motivational direction. In a further study, we carried out two probe recognition experiments to examine the interaction during sentence comprehension; in both, the critical probe was the word referring to the target of the action (e.g., “meat”). In the first experiment, participants had to recognize the probe word presented 1500 milliseconds after sentence offset, while for the second one, the delay was 500 milliseconds. Results showed that at 1500 ms, target recognition took significantly more time for negated avoidance sentences than for the other conditions. Therefore, representing negated avoidance sentences seems to imply more complex processing, as avoidance verbs would be implicitly negative. By contrast, at the 500 ms delay, negation impaired target recognition for both approach and avoidance sentences, suggesting an unspecific inhibitory effect of negation at that sentence processing stage. Implication of these results for both research on negation and in action understanding are discussed.

Moral reasoning is the process of asking moral questions and answering them

Reasoning is the iterative, path-dependent process of asking questions and answering them. Moral reasoning is a species of such reasoning, so it is a matter of asking and answering moral questions, which requires both creativity and curiosity. As such, interventions and practices that help people ask more and better moral questions promise to improve moral reasoning.

Brain Inhibitory Mechanisms Are Involved in the Processing of Sentential Negation, Regardless of Its Content. Evidence From EEG Theta and Beta Rhythms

The two-step process account of negation understanding posits an initial representation of the negated events, followed by a representation of the actual state of events. On the other hand, behavioral and neurophysiological studies provided evidence that linguistic negation suppresses or reduces the activation of the negated events, contributing to shift attention to the actual state of events. However, the specific mechanism of this suppression is poorly known. Recently, based on the brain organization principle of neural reuse (Anderson, 2010), it has been proposed that understanding linguistic negation partially relies upon the neurophysiological mechanisms of response inhibition. Specifically, it was reported that negated action-related sentences modulate EEG signatures of response inhibition (de Vega et al., 2016; Beltrán et al., 2018). In the current EEG study, we ponder whether the reusing of response inhibition processes by negation is constrained to action-related contents or consists of a more general-purpose mechanism. To this end, we employed the same dual-task paradigm as in our prior study—a Go/NoGo task embedded into a sentence comprehension task—but this time including both action and non-action sentences. The results confirmed that the increase of theta power elicited by NoGo trials was modulated by negative sentences, compared to their affirmative counterparts, and this polarity effect was statistically similar for both action- and non-action-related sentences. Thus, a general-purpose inhibitory control mechanism, rather than one specific for action language, is likely operating in the comprehension of sentential negation to produce the transition between alternative representations.

Cancellation, negation, and rejection

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, & Klauer, 2016a) can be classified as being produced by (a) a conversational implicature, (b) a (probabilistic) presupposition failure, or (c) a conventional implicature. After considering several alternative hypotheses, and the accumulating evidence from other studies as well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content.

Thinking About the Opposite of What Is Said: Counterfactual Conditionals and Symbolic or Alternate Simulations of Negation

When people understand a counterfactual such as "if the flowers had been roses, the trees would have been orange trees," they think about the conjecture, "there were roses and orange trees," and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, "poppies and apple trees," or whether models can contain symbols, for example, "no roses and no orange trees." We report the discovery of an inference-to-alternates effect-a tendency to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, "there were no orange trees, therefore there were poppies." Nine experiments show the inference-to-alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation.

Negation in context: Evidence from the visual world paradigm

Literature assumes that negation is more difficult to understand than affirmation, but this might depend on the pragmatic context. The goal of this paper is to show that pragmatic knowledge modulates the unfolding processing of negation due to the previous activation of the negated situation. To test this, we used the visual world paradigm. In this task, we presented affirmative (e.g., her dad was rich) and negative sentences (e.g., her dad was not poor) while viewing two images of the affirmed and denied entities. The critical sentence in each item was preceded by one of three types of contexts: an inconsistent context (e.g., She supposed that her dad had little savings) that activates the negated situation (a poor man), a consistent context (e.g., She supposed that her dad had enough savings) that activates the actual situation (a rich man), or a neutral context (e.g., her dad lived on the other side of town) that activates neither of the two models previously suggested. The results corroborated our hypothesis. Pragmatics is implicated in the unfolding processing of negation. We found an increase in fixations on the target compared to the baseline for negative sentences at 800 ms in the neutral context, 600 ms in the inconsistent context, and 1450 ms in the consistent context. Thus, when the negated situation has been previously introduced via an inconsistent context, negation is facilitated.

Visual content of words delays negation

Many studies have shown the advantage of processing visualizable words over non-visualizables due to the associated image code. The present paper reports the case of negation in which imagery could slow down processing. Negation reverses the truth value of a proposition from false to true or vice versa. Consequently, negation works only on propositions (reversing their truth value) and cannot apply directly to other forms of knowledge representation such as images (although they can be veridical or not). This leads to a paradoxical hypothesis: despite the advantage of visualizable words for general processing, the negation of clauses containing words related to the representation of an image would be more difficult than negation containing non-visualizable words. Two experiments support this hypothesis by showing that sentences with a previously negated visualizable word took longer to be read than sentences with previously negated non-visualizable words. The results suggest that a verbal code is used to process negation.

Causal reasoning with mental models

This paper outlines the model-based theory of causal reasoning. It postulates that the core meanings of causal assertions are deterministic and refer to temporally-ordered sets of possibilities: A causes B to occur means that given A, B occurs, whereas A enables B to occur means that given A, it is possible for B to occur. The paper shows how mental models represent such assertions, and how these models underlie deductive, inductive, and abductive reasoning yielding explanations. It reviews evidence both to corroborate the theory and to account for phenomena sometimes taken to be incompatible with it. Finally, it reviews neuroscience evidence indicating that mental models for causal inference are implemented within lateral prefrontal cortex.

The negations of conjunctions, conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.

Kinematic mental simulations in abduction and deduction

We present a theory, and its computer implementation, of how mental simulations underlie the abductions of informal algorithms and deductions from these algorithms. Three experiments tested the theory's predictions, using an environment of a single railway track and a siding. This environment is akin to a universal Turing machine, but it is simple enough for nonprogrammers to use. Participants solved problems that required use of the siding to rearrange the order of cars in a train (experiment 1). Participants abduced and described in their own words algorithms that solved such problems for trains of any length, and, as the use of simulation predicts, they favored "while-loops" over "for-loops" in their descriptions (experiment 2). Given descriptions of loops of procedures, participants deduced the consequences for given trains of six cars, doing so without access to the railway environment (experiment 3). As the theory predicts, difficulty in rearranging trains depends on the numbers of moves and cars to be moved, whereas in formulating an algorithm and deducing its consequences, it depends on the Kolmogorov complexity of the algorithm. Overall, the results corroborated the use of a kinematic mental model in creating and testing informal algorithms and showed that individuals differ reliably in the ability to carry out these tasks.

The compatibility heuristic in non-categorical hypothetical reasoning: inferences between conditionals and disjunctions

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for 'A only if B' conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for 'if and only if A B' bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., 'A or B, therefore if C D' (Experiment 4), and between universals 'All A's are B's' and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.