Andrea E. Martin

Publications

Displaying 1 - 20 of 20
  • Coopmans, C. W., De Hoop, H., Kaushik, K., Hagoort, P., & Martin, A. E. (2021). Structure-(in)dependent interpretation of phrases in humans and LSTMs. In Proceedings of the Society for Computation in Linguistics (SCiL 2021) (pp. 459-463).

    Abstract

    In this study, we compared the performance of a long short-term memory (LSTM) neural network to the behavior of human participants on a language task that requires hierarchically structured knowledge. We show that humans interpret ambiguous noun phrases, such as second blue ball, in line with their hierarchical constituent structure. LSTMs, instead, only do
    so after unambiguous training, and they do not systematically generalize to novel items. Overall, the results of our simulations indicate that a model can behave hierarchically without relying on hierarchical constituent structure.
  • Doumas, L. A. A., & Martin, A. E. (2021). A model for learning structured representations of similarity and relative magnitude from experience. Current Opinion in Behavioral Sciences, 37, 158-166. doi:10.1016/j.cobeha.2021.01.001.

    Abstract

    How a system represents information tightly constrains the kinds of problems it can solve. Humans routinely solve problems that appear to require abstract representations of stimulus properties and relations. How we acquire such representations has central importance in an account of human cognition. We briefly describe a theory of how a system can learn invariant responses to instances of similarity and relative magnitude, and how structured, relational representations can be learned from initially unstructured inputs. Two operations, comparing distributed representations and learning from the concomitant network dynamics in time, underpin the ability to learn these representations and to respond to invariance in the environment. Comparing analog representations of absolute magnitude produces invariant signals that carry information about similarity and relative magnitude. We describe how a system can then use this information to bootstrap learning structured (i.e., symbolic) concepts of relative magnitude from experience without assuming such representations a priori.
  • Guest, O., & Martin, A. E. (2021). How computational modeling can force theory building in psychological science. Perspectives on Psychological Science, 16(4), 789-802. doi:10.1177/1745691620970585.

    Abstract

    Psychology endeavors to develop theories of human capacities and behaviors on the basis of a variety of methodologies and dependent measures. We argue that one of the most divisive factors in psychological science is whether researchers choose to use computational modeling of theories (over and above data) during the scientific-inference process. Modeling is undervalued yet holds promise for advancing psychological science. The inherent demands of computational modeling guide us toward better science by forcing us to conceptually analyze, specify, and formalize intuitions that otherwise remain unexamined—what we dub open theory. Constraining our inference process through modeling enables us to build explanatory and predictive theories. Here, we present scientific inference in psychology as a path function in which each step shapes the next. Computational modeling can constrain these steps, thus advancing scientific inference over and above the stewardship of experimental practice (e.g., preregistration). If psychology continues to eschew computational modeling, we predict more replicability crises and persistent failure at coherent theory building. This is because without formal modeling we lack open and transparent theorizing. We also explain how to formalize, specify, and implement a computational model, emphasizing that the advantages of modeling can be achieved by anyone with benefit to all.
  • Puebla, G., Martin, A. E., & Doumas, L. A. A. (2021). The relational processing limits of classic and contemporary neural network models of language processing. Language, Cognition and Neuroscience, 36(2), 240-254. doi:10.1080/23273798.2020.1821906.

    Abstract

    Whether neural networks can capture relational knowledge is a matter of long-standing controversy. Recently, some researchers have argued that (1) classic connectionist models can handle relational structure and (2) the success of deep learning approaches to natural language processing suggests that structured representations are unnecessary to model human language. We tested the Story Gestalt model, a classic connectionist model of text comprehension, and a Sequence-to-Sequence with Attention model, a modern deep learning architecture for natural language processing. Both models were trained to answer questions about stories based on abstract thematic roles. Two simulations varied the statistical structure of new stories while keeping their relational structure intact. The performance of each model fell below chance at least under one manipulation. We argue that both models fail our tests because they can't perform dynamic binding. These results cast doubts on the suitability of traditional neural networks for explaining relational reasoning and language processing phenomena.

    Additional information

    supplementary material
  • Ten Oever, S., & Martin, A. E. (2021). An oscillating computational model can track pseudo-rhythmic speech by using linguistic predictions. eLife, 10: e68066. doi:10.7554/eLife.68066.

    Abstract

    Neuronal oscillations putatively track speech in order to optimize sensory processing. However, it is unclear how isochronous brain oscillations can track pseudo-rhythmic speech input. Here we propose that oscillations can track pseudo-rhythmic speech when considering that speech time is dependent on content-based predictions flowing from internal language models. We show that temporal dynamics of speech are dependent on the predictability of words in a sentence. A computational model including oscillations, feedback, and inhibition is able to track pseudo-rhythmic speech input. As the model processes, it generates temporal phase codes, which are a candidate mechanism for carrying information forward in time. The model is optimally sensitive to the natural temporal speech dynamics and can explain empirical data on temporal speech illusions. Our results suggest that speech tracking does not have to rely only on the acoustics but could also exploit ongoing interactions between oscillations and constraints flowing from internal language models.
  • Brennan, J. R., & Martin, A. E. (2019). Phase synchronization varies systematically with linguistic structure composition. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 375(1791): 20190305. doi:10.1098/rstb.2019.0305.

    Abstract

    Computation in neuronal assemblies is putatively reflected in the excitatory and inhibitory cycles of activation distributed throughout the brain. In speech and language processing, coordination of these cycles resulting in phase synchronization has been argued to reflect the integration of information on different timescales (e.g. segmenting acoustics signals to phonemic and syllabic representations; (Giraud and Poeppel 2012 Nat. Neurosci.15, 511 (doi:10.1038/nn.3063)). A natural extension of this claim is that phase synchronization functions similarly to support the inference of more abstract higher-level linguistic structures (Martin 2016 Front. Psychol.7, 120; Martin and Doumas 2017 PLoS Biol. 15, e2000663 (doi:10.1371/journal.pbio.2000663); Martin and Doumas. 2019 Curr. Opin. Behav. Sci.29, 77–83 (doi:10.1016/j.cobeha.2019.04.008)). Hale et al. (Hale et al. 2018 Finding syntax in human encephalography with beam search. arXiv 1806.04127 (http://arxiv.org/abs/1806.04127)) showed that syntactically driven parsing decisions predict electroencephalography (EEG) responses in the time domain; here we ask whether phase synchronization in the form of either inter-trial phrase coherence or cross-frequency coupling (CFC) between high-frequency (i.e. gamma) bursts and lower-frequency carrier signals (i.e. delta, theta), changes as the linguistic structures of compositional meaning (viz., bracket completions, as denoted by the onset of words that complete phrases) accrue. We use a naturalistic story-listening EEG dataset from Hale et al. to assess the relationship between linguistic structure and phase alignment. We observe increased phase synchronization as a function of phrase counts in the delta, theta, and gamma bands, especially for function words. A more complex pattern emerged for CFC as phrase count changed, possibly related to the lack of a one-to-one mapping between ‘size’ of linguistic structure and frequency band—an assumption that is tacit in recent frameworks. These results emphasize the important role that phase synchronization, desynchronization, and thus, inhibition, play in the construction of compositional meaning by distributed neural networks in the brain.
  • Martin, A. E., & Baggio, G. (2019). Modeling meaning composition from formalism to mechanism. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 375: 20190298. doi:10.1098/rstb.2019.0298.

    Abstract

    Human thought and language have extraordinary expressive power because meaningful parts can be assembled into more complex semantic structures. This partly underlies our ability to compose meanings into endlessly novel configurations, and sets us apart from other species and current computing devices. Crucially, human behaviour, including language use and linguistic data, indicates that composing parts into complex structures does not threaten the existence of constituent parts as independent units in the system: parts and wholes exist simultaneously yet independently from one another in the mind and brain. This independence is evident in human behaviour, but it seems at odds with what is known about the brain's exquisite sensitivity to statistical patterns: everyday language use is productive and expressive precisely because it can go beyond statistical regularities. Formal theories in philosophy and linguistics explain this fact by assuming that language and thought are compositional: systems of representations that separate a variable (or role) from its values (fillers), such that the meaning of a complex expression is a function of the values assigned to the variables. The debate on whether and how compositional systems could be implemented in minds, brains and machines remains vigorous. However, it has not yet resulted in mechanistic models of semantic composition: how, then, are the constituents of thoughts and sentences put and held together? We review and discuss current efforts at understanding this problem, and we chart possible routes for future research.
  • Martin, A. E., & Doumas, L. A. A. (2019). Tensors and compositionality in neural systems. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 375(1791): 20190306. doi:10.1098/rstb.2019.0306.

    Abstract

    Neither neurobiological nor process models of meaning composition specify the operator through which constituent parts are bound together into compositional structures. In this paper, we argue that a neurophysiological computation system cannot achieve the compositionality exhibited in human thought and language if it were to rely on a multiplicative operator to perform binding, as the tensor product (TP)-based systems that have been widely adopted in cognitive science, neuroscience and artificial intelligence do. We show via simulation and two behavioural experiments that TPs violate variable-value independence, but human behaviour does not. Specifically, TPs fail to capture that in the statements fuzzy cactus and fuzzy penguin, both cactus and penguin are predicated by fuzzy(x) and belong to the set of fuzzy things, rendering these arguments similar to each other. Consistent with that thesis, people judged arguments that shared the same role to be similar, even when those arguments themselves (e.g., cacti and penguins) were judged to be dissimilar when in isolation. By contrast, the similarity of the TPs representing fuzzy(cactus) and fuzzy(penguin) was determined by the similarity of the arguments, which in this case approaches zero. Based on these results, we argue that neural systems that use TPs for binding cannot approximate how the human mind and brain represent compositional information during processing. We describe a contrasting binding mechanism that any physiological or artificial neural system could use to maintain independence between a role and its argument, a prerequisite for compositionality and, thus, for instantiating the expressive power of human thought and language in a neural system.

    Additional information

    Supplemental Material
  • Martin, A. E., & Doumas, L. A. A. (2019). Predicate learning in neural systems: Using oscillations to discover latent structure. Current Opinion in Behavioral Sciences, 29, 77-83. doi:10.1016/j.cobeha.2019.04.008.

    Abstract

    Humans learn to represent complex structures (e.g. natural language, music, mathematics) from experience with their environments. Often such structures are latent, hidden, or not encoded in statistics about sensory representations alone. Accounts of human cognition have long emphasized the importance of structured representations, yet the majority of contemporary neural networks do not learn structure from experience. Here, we describe one way that structured, functionally symbolic representations can be instantiated in an artificial neural network. Then, we describe how such latent structures (viz. predicates) can be learned from experience with unstructured data. Our approach exploits two principles from psychology and neuroscience: comparison of representations, and the naturally occurring dynamic properties of distributed computing across neuronal assemblies (viz. neural oscillations). We discuss how the ability to learn predicates from experience, to represent information compositionally, and to extrapolate knowledge to unseen data is core to understanding and modeling the most complex human behaviors (e.g. relational reasoning, analogy, language processing, game play).
  • Doumas, L. A. A., Hamer, A., Puebla, G., & Martin, A. E. (2017). A theory of the detection and learning of structured representations of similarity and relative magnitude. In G. Gunzelmann, A. Howes, T. Tenbrink, & E. Davelaar (Eds.), Proceedings of the 39th Annual Conference of the Cognitive Science Society (CogSci 2017) (pp. 1955-1960). Austin, TX: Cognitive Science Society.

    Abstract

    Responding to similarity, difference, and relative magnitude (SDM) is ubiquitous in the animal kingdom. However, humans seem unique in the ability to represent relative magnitude (‘more’/‘less’) and similarity (‘same’/‘different’) as abstract relations that take arguments (e.g., greater-than (x,y)). While many models use structured relational representations of magnitude and similarity, little progress has been made on how these representations arise. Models that developuse these representations assume access to computations of similarity and magnitude a priori, either encoded as features or as output of evaluation operators. We detail a mechanism for producing invariant responses to “same”, “different”, “more”, and “less” which can be exploited to compute similarity and magnitude as an evaluation operator. Using DORA (Doumas, Hummel, & Sandhofer, 2008), these invariant responses can serve be used to learn structured relational representations of relative magnitude and similarity from pixel images of simple shapes
  • Ito, A., Martin, A. E., & Nieuwland, M. S. (2017). How robust are prediction effects in language comprehension? Failure to replicate article-elicited N400 effects. Language, Cognition and Neuroscience, 32, 954-965. doi:10.1080/23273798.2016.1242761.

    Abstract

    Current psycholinguistic theory proffers prediction as a central, explanatory mechanism in language
    processing. However, widely-replicated prediction effects may not mean that prediction is
    necessary in language processing. As a case in point, C. D. Martin et al. [2013. Bilinguals reading
    in their second language do not predict upcoming words as native readers do.
    Journal of
    Memory and Language, 69
    (4), 574

    588. doi:10.1016/j.jml.2013.08.001] reported ERP evidence for
    prediction in native- but not in non-native speakers. Articles mismatching an expected noun
    elicited larger negativity in the N400 time window compared to articles matching the expected
    noun in native speakers only. We attempted to replicate these findings, but found no evidence
    for prediction irrespective of language nativeness. We argue that pre-activation of phonological
    form of upcoming nouns, as evidenced in article-elicited effects, may not be a robust
    phenomenon. A view of prediction as a necessary computation in language comprehension
    must be re-evaluated.
  • Ito, A., Martin, A. E., & Nieuwland, M. S. (2017). On predicting form and meaning in a second language. Journal of Experimental Psychology: Learning, Memory, and Cognition, 43(4), 635-652. doi:10.1037/xlm0000315.

    Abstract

    We used event-related potentials (ERP) to investigate whether Spanish−English bilinguals preactivate form and meaning of predictable words. Participants read high-cloze sentence contexts (e.g., “The student is going to the library to borrow a . . .”), followed by the predictable word (book), a word that was form-related (hook) or semantically related (page) to the predictable word, or an unrelated word (sofa). Word stimulus onset synchrony (SOA) was 500 ms (Experiment 1) or 700 ms (Experiment 2). In both experiments, all nonpredictable words elicited classic N400 effects. Form-related and unrelated words elicited similar N400 effects. Semantically related words elicited smaller N400s than unrelated words, which however, did not depend on cloze value of the predictable word. Thus, we found no N400 evidence for preactivation of form or meaning at either SOA, unlike native-speaker results (Ito, Corley et al., 2016). However, non-native speakers did show the post-N400 posterior positivity (LPC effect) for form-related words like native speakers, but only at the slower SOA. This LPC effect increased gradually with cloze value of the predictable word. We do not interpret this effect as necessarily demonstrating prediction, but rather as evincing combined effects of top-down activation (contextual meaning) and bottom-up activation (form similarity) that result in activation of unseen words that fit the context well, thereby leading to an interpretation conflict reflected in the LPC. Although there was no evidence that non-native speakers preactivate form or meaning, non-native speakers nonetheless appear to use bottom-up and top-down information to constrain incremental interpretation much like native speakers do.
  • Ito, A., Martin, A. E., & Nieuwland, M. S. (2017). Why the A/AN prediction effect may be hard to replicate: A rebuttal to DeLong, Urbach & Kutas (2017). Language, Cognition and Neuroscience, 32(8), 974-983. doi:10.1080/23273798.2017.1323112.
  • Martin, A. E., & Doumas, L. A. A. (2017). A mechanism for the cortical computation of hierarchical linguistic structure. PLoS Biology, 15(3): e2000663. doi:10.1371/journal.pbio.2000663.

    Abstract

    Biological systems often detect species-specific signals in the environment. In humans, speech and language are species-specific signals of fundamental biological importance. To detect the linguistic signal, human brains must form hierarchical representations from a sequence of perceptual inputs distributed in time. What mechanism underlies this ability? One hypothesis is that the brain repurposed an available neurobiological mechanism when hierarchical linguistic representation became an efficient solution to a computational problem posed to the organism. Under such an account, a single mechanism must have the capacity to perform multiple, functionally related computations, e.g., detect the linguistic signal and perform other cognitive functions, while, ideally, oscillating like the human brain. We show that a computational model of analogy, built for an entirely different purpose—learning relational reasoning—processes sentences, represents their meaning, and, crucially, exhibits oscillatory activation patterns resembling cortical signals elicited by the same stimuli. Such redundancy in the cortical and machine signals is indicative of formal and mechanistic alignment between representational structure building and “cortical” oscillations. By inductive inference, this synergy suggests that the cortical signal reflects structure generation, just as the machine signal does. A single mechanism—using time to encode information across a layered network—generates the kind of (de)compositional representational hierarchy that is crucial for human language and offers a mechanistic linking hypothesis between linguistic representation and cortical computation
  • Martin, A. E., Huettig, F., & Nieuwland, M. S. (2017). Can structural priming answer the important questions about language? A commentary on Branigan and Pickering "An experimental approach to linguistic representation". Behavioral and Brain Sciences, 40: e304. doi:10.1017/S0140525X17000528.

    Abstract

    While structural priming makes a valuable contribution to psycholinguistics, it does not allow direct observation of representation, nor escape “source ambiguity.” Structural priming taps into implicit memory representations and processes that may differ from what is used online. We question whether implicit memory for language can and should be equated with linguistic representation or with language processing.
  • Martin, A. E., Monahan, P. J., & Samuel, A. G. (2017). Prediction of agreement and phonetic overlap shape sublexical identification. Language and Speech, 60(3), 356-376. doi:10.1177/0023830916650714.

    Abstract

    The mapping between the physical speech signal and our internal representations is rarely straightforward. When faced with uncertainty, higher-order information is used to parse the signal and because of this, the lexicon and some aspects of sentential context have been shown to modulate the identification of ambiguous phonetic segments. Here, using a phoneme identification task (i.e., participants judged whether they heard [o] or [a] at the end of an adjective in a noun–adjective sequence), we asked whether grammatical gender cues influence phonetic identification and if this influence is shaped by the phonetic properties of the agreeing elements. In three experiments, we show that phrase-level gender agreement in Spanish affects the identification of ambiguous adjective-final vowels. Moreover, this effect is strongest when the phonetic characteristics of the element triggering agreement and the phonetic form of the agreeing element are identical. Our data are consistent with models wherein listeners generate specific predictions based on the interplay of underlying morphosyntactic knowledge and surface phonetic cues.
  • Nieuwland, M. S., & Martin, A. E. (2017). Neural oscillations and a nascent corticohippocampal theory of reference. Journal of Cognitive Neuroscience, 29(5), 896-910. doi:10.1162/jocn_a_01091.

    Abstract

    The ability to use words to refer to the world is vital to the communicative power of human language. In particular, the anaphoric use of words to refer to previously mentioned concepts (antecedents) allows dialogue to be coherent and meaningful. Psycholinguistic theory posits that anaphor comprehension involves reactivating a memory representation of the antecedent. Whereas this implies the involvement of recognition memory, or the mnemonic sub-routines by which people distinguish old from new, the neural processes for reference resolution are largely unknown. Here, we report time-frequency analysis of four EEG experiments to reveal the increased coupling of functional neural systems associated with referentially coherent expressions compared to referentially problematic expressions. Despite varying in modality, language, and type of referential expression, all experiments showed larger gamma-band power for referentially coherent expressions compared to referentially problematic expressions. Beamformer analysis in high-density Experiment 4 localised the gamma-band increase to posterior parietal cortex around 400-600 ms after anaphor-onset and to frontaltemporal cortex around 500-1000 ms. We argue that the observed gamma-band power increases reflect successful referential binding and resolution, which links incoming information to antecedents through an interaction between the brain’s recognition memory networks and frontal-temporal language network. We integrate these findings with previous results from patient and neuroimaging studies, and we outline a nascent cortico-hippocampal theory of reference.
  • Martin, A. E., Nieuwland, M. S., & Carreiras, M. (2012). Event-related brain potentials index cue-based retrieval interference during sentence comprehension. NeuroImage, 59(2), 1859-1869. doi:10.1016/j.neuroimage.2011.08.057.

    Abstract

    Successful language use requires access to products of past processing within an evolving discourse. A central issue for any neurocognitive theory of language then concerns the role of memory variables during language processing. Under a cue-based retrieval account of language comprehension, linguistic dependency resolution (e.g., retrieving antecedents) is subject to interference from other information in the sentence, especially information that occurs between the words that form the dependency (e.g., between the antecedent and the retrieval site). Retrieval interference may then shape processing complexity as a function of the match of the information at retrieval with the antecedent versus other recent or similar items in memory. To address these issues, we studied the online processing of ellipsis in Castilian Spanish, a language with morphological gender agreement. We recorded event-related brain potentials while participants read sentences containing noun-phrase ellipsis indicated by the determiner otro/a (‘another’). These determiners had a grammatically correct or incorrect gender with respect to their antecedent nouns that occurred earlier in the sentence. Moreover, between each antecedent and determiner, another noun phrase occurred that was structurally unavailable as an antecedent and that matched or mismatched the gender of the antecedent (i.e., a local agreement attractor). In contrast to extant P600 results on agreement violation processing, and inconsistent with predictions from neurocognitive models of sentence processing, grammatically incorrect determiners evoked a sustained, broadly distributed negativity compared to correct ones between 400 and 1000 ms after word onset, possibly related to sustained negativities as observed for referential processing difficulties. Crucially, this effect was modulated by the attractor: an increased negativity was observed for grammatically correct determiners that did not match the gender of the attractor, suggesting that structurally unavailable noun phrases were at least temporarily considered for grammatically correct ellipsis. These results constitute the first ERP evidence for cue-based retrieval interference during comprehension of grammatical sentences.
  • Nieuwland, M. S., Martin, A. E., & Carreiras, M. (2012). Brain regions that process case: Evidence from basque. Human Brain Mapping, 33(11), 2509-2520. doi:10.1002/hbm.21377.

    Abstract

    The aim of this event-related fMRI study was to investigate the cortical networks involved in case processing, an operation that is crucial to language comprehension yet whose neural underpinnings are not well-understood. What is the relationship of these networks to those that serve other aspects of syntactic and semantic processing? Participants read Basque sentences that contained case violations, number agreement violations or semantic anomalies, or that were both syntactically and semantically correct. Case violations elicited activity increases, compared to correct control sentences, in a set of parietal regions including the posterior cingulate, the precuneus, and the left and right inferior parietal lobules. Number agreement violations also elicited activity increases in left and right inferior parietal regions, and additional activations in the left and right middle frontal gyrus. Regions-of-interest analyses showed that almost all of the clusters that were responsive to case or number agreement violations did not differentiate between these two. In contrast, the left and right anterior inferior frontal gyrus and the dorsomedial prefrontal cortex were only sensitive to semantic violations. Our results suggest that whereas syntactic and semantic anomalies clearly recruit distinct neural circuits, case, and number violations recruit largely overlapping neural circuits and that the distinction between the two rests on the relative contributions of parietal and prefrontal regions, respectively. Furthermore, our results are consistent with recently reported contributions of bilateral parietal and dorsolateral brain regions to syntactic processing, pointing towards potential extensions of current neurocognitive theories of language. Hum Brain Mapp, 2012. © 2011 Wiley Periodicals, Inc.
  • Nieuwland, M. S., & Martin, A. E. (2012). If the real world were irrelevant, so to speak: The role of propositional truth-value in counterfactual sentence comprehension. Cognition, 122(1), 102-109. doi:10.1016/j.cognition.2011.09.001.

    Abstract

    Propositional truth-value can be a defining feature of a sentence’s relevance to the unfolding discourse, and establishing propositional truth-value in context can be key to successful interpretation. In the current study, we investigate its role in the comprehension of counterfactual conditionals, which describe imaginary consequences of hypothetical events, and are thought to require keeping in mind both what is true and what is false. Pre-stored real-world knowledge may therefore intrude upon and delay counterfactual comprehension, which is predicted by some accounts of discourse comprehension, and has been observed during online comprehension. The impact of propositional truth-value may thus be delayed in counterfactual conditionals, as also claimed for sentences containing other types of logical operators (e.g., negation, scalar quantifiers). In an event-related potential (ERP) experiment, we investigated the impact of propositional truth-value when described consequences are both true and predictable given the counterfactual premise. False words elicited larger N400 ERPs than true words, in negated counterfactual sentences (e.g., “If N.A.S.A. had not developed its Apollo Project, the first country to land on the moon would have been Russia/America”) and real-world sentences (e.g., “Because N.A.S.A. developed its Apollo Project, the first country to land on the moon was America/Russia”) alike. These indistinguishable N400 effects of propositional truth-value, elicited by opposite word pairs, argue against disruptions by real-world knowledge during counterfactual comprehension, and suggest that incoming words are mapped onto the counterfactual context without any delay. Thus, provided a sufficiently constraining context, propositional truth-value rapidly impacts ongoing semantic processing, be the proposition factual or counterfactual.

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