Cognitive Modeling in Computational Rhetoric: Litotes, Containment and the Unexcluded Middle Jelena Mitrovic´1 a, Cliff O’Reilly2 b, Randy Allen Harris3 c and Michael Granitzer1 d 1Faculty of Computer Science and Mathematics, University of Passau, Germany 2Birkbeck College, University of London, U.K. 3Department of English Language and Literature, University of Waterloo, Canada, U.S.A. [email protected], [email protected], [email protected], [email protected] Keywords: Litotes, Computational Rhetoric, Cognitive Modeling, Ontology, Image Schema, Unexcluded Middle. Abstract: The focus of our study is the rhetorical figure litotes and its cognitive modeling. This figure is formed by a contrary term that emphatically accentuates a positive, e.g. He is not exactly an idiot (said of Albert Einstein). Lawrence Horn’s illumination of the Law of Excluded Middle and its relationship to litotes by creating an Unexcluded Middle is central to our ideas and we correlate this to Image Schema theories developed by Mark Johnson, George Lakoff and Rafael Nu´nez˜ – specifically the schema of CONTAINMENT. The distinction be- tween contrary and contradictory opposition is described. We extend the assessment of the Excluded Middle from the perspective of Image Schema theory into the realm of the Unexcluded Middle and draw a represen- tation of the layout of containers and analogous concept-activation. Lastly, we create and present an OWL ontology and publish it online. 1 INTRODUCTION tion and understanding of rhetorical figures, their as- sociated cognitive machinery and computational ap- We argue for the integration of rhetorical studies, plicability. cognitive science, computational modeling, and Nat- In this paper we connect the realm of rhetorical ural language processing (NLP), by way of an ex- studies to the domain of Image Schema theory. As tended example, the unjustly neglected rhetorical fig- Dewell has said: “...language plays a much greater ure, litotes. role in the development of image schemas than is of- Litotes is a figure in which we say less but mean ten assumed, contributing not only to cross-linguistic more (“minus dicimus et plus significamus” (Miguel, variation but also to some universal similarities in 1990)) and can be placed in the Pragmatic context un- the structure of image schemas” (Dewell, 2005). We der Implicature – the difference between what is said are especially concerned with the universal schema by a speaker and what is intended1. Litotes is as ubiq- known as containment, which gives a valuable pur- uitous as any of the more famous rhetorical figures chase on litotes. such as metaphor and irony, and yet not well studied The Law of the Excluded Middle is a primary el- from a computational perspective. Despite this ne- ement of logical thought and a variant extension of glect, we hold that research on its function, role and this law – named the Unexcluded Middle – effectively importance promises headway in the rich new field bridges litotic understatement and cognitive concept- of figure analysis in Computational Rhetoric, an area activation, i.e. the neuronal activity resulting in con- of study which brings together computer scientists, scious or subconscious understanding of a concept. rhetoricians, psychologists, philologists, literary crit- In section 2 we offer some background on litotes, ics and information scientists working on the detec- a more detailed analysis of the Unexcluded Middle, a the Image Schema CONTAINMENT and the onto- https://orcid.org/0000-0003-3220-8749 logical approach to modeling litotes. Section 3 gives b https://orcid.org/0000-0001-8002-5336 c an analysis of how these concepts are intertwined in https://orcid.org/0000-0002-9324-1879 litotes while in section 4 we provide an OWL ontol- d https://orcid.org/0000-0003-3566-5507 1 ogy of litotes. Conclusions and Future work consid- For a defining overview of rhetorical figures including erations are given in the last two sections of the paper. litotes see (Harris and Di Marco, 2017) 2 BACKGROUND biggest”, or at least “really big”. Sometimes, how- ever, repeating the negative has less emphatic sense. 2.1 Litotes For instance, compare the two sentences, “Lupita Ny- ong’o is not unattractive” (with a negator and a negat- Litotes is a rhetorical figure in which a state- ing prefix) and “Lupita Nyong’o is not ugly” (with a ment is made emphatic by denying a con- negator and a negatively valenced adjective). The first trary. A straightforward example from Henry one is mildly complimentary about her appearance, Peacham’s The Garden of Eloquence (1593) is the second more emphatic. And with the following “he is not the wisest man in the world” which has a example, which pushes the disavowal of the adjective meaning similar to “he is a fool” (Lanham, 1991). to an extreme, the compliment approaches perfection: It is a form of understatement, also known as “Lupita Nyong’o is the furthest thing from ugly.” Deminutio to Latin pre-Christian scholars, but the Computational modeling of litotes has to take into term comes to us from the Greek meaning “smooth” consideration its many characteristics, negation being or “plain”: litothc. An example of litotes appears in the most prominent. Negation has been treated differ- the early handbook erroneously attributed to Cicero, ently in Linguistics and Rhetoric, as well as in Prag- the Rhetoric ad Herennium (Cicero, 1954): matics, where it has a strong effect (Taboada et al., 2017). Likewise, a rhetorical figure such as Antithesis “his father left him a patrimony that was – I has been seen as very effective and even persuasive, do not wish to exaggerate – not the smallest” precisely due to the presence of negation, as well as Cicero expresses the point of mitigating a posi- opposition. We see litotes as a figure that can also tive but nevertheless getting across the message in- play a persuasive role in arguments, therefore its de- tended, i.e. that the legacy in question was large in- tection should be included in argument mining sys- deed. There is, in short, some level of irony at work tems (Mitrovic´ et al., 2017). with litotes, and interpretation requires a reconstruc- tion of the speaker’s intention. The impact of litotes 2.2 Unexcluded Middle derives from speaking plainly about a subject while, at the same time, contradicting a negative term to In logic, the Law of Excluded Middle, dating at enhance the positive. Its usefulness as a means for least to Aristotle’s discussion of the principle of non- understatement, modesty and insult leads to signifi- contradiction in On Interpretation (Aristotle, 1938), cant usage and an almost ubiquitous position in lan- states that for any proposition, either that proposition guage and culture (Shovel, 2015). Its prominence has is true or its negation is true. It is the third of the three brought a few interesting studies in more recent times classic laws of thought. This, now (in)famous quote (Hermann et al., 2013; Yuan, 2017) from a former United States’ president illustrates us- Horn examines the figure in great detail (Horn, age of the excluded middle in modern practice : 2017) and differentiates between two important con- (1) Either you are with us or you are with the cepts - contrariety and contradiction. A contradictory terrorists (George W. Bush) opposition is binary, e.g. black versus white or green versus not green, whereas a contrary opposition can Using propositional logic notation to reflect the logic allow room for things to lie in-between, e.g. truthful of the terms and arguments involved we can say that versus untruthful or comfortable versus uncomfort- P _ Q becomes P _:P (P represents being “with us” able. Nuance, context and vagueness are important and Q represents being “with the terrorists”). By im- factors that determine the impact of the differences in plication anyone not with “us” must be with “the ter- contrary oppositions. rorists”. We illustrate this in Figure 1 – we transi- Litotes aligns both with the principles of logic (the tion from a three member set fus,terrorists,neither us negation of a negative is a positive) and the prin- nor terroristsg to a two-member set fus,terroristsg and ciples of style (no repetition is null). Repetitions the middle is effectively excluded from being (“po- work chiefly in an additive way, but the main is ad- lar contraries p and q become mutually exhaustive as ditive, familiar in the iconicity principle of quantity – well as mutually inconsistent” (Horn, 2017)). more language corresponds to more conceptual mat- ter (Givon, 1991). That is where the emphasis comes in. The two negatives in this case are not just positive, they are emphatically positive. Denotatively, “not the smallest” means that there is at least one other quan- tity that is smaller, the not cancelling out the superla- tive. Rhetorically, it means something more like “the Figure 1: Transition to Excluded Middle. There is a further twist to this pattern called the Unexcluded Middle. This aspect of the litotic form can be seen in the following example: (2) I’m not happy but I’m not unhappy about it. (The History Boys, Alan Bennett) The speaker is neither happy nor unhappy which vio- Figure 3: When two negatives don’t make a positive, repro- lates the law of non-contradiction, but rhetorically the duced from (Blutner et al., 2004). meaning is that happiness is irrelevant to the situa- tion. Pragmatically, we may also say that (despite the Just as regarding affixal negation (the binary nature of the adjectives) happiness can form “notorious not un- construction” (Horn, 2017)) a contrary opposition, not contradictory one, so that such as “not unhappy”, we can include a similar the speaker can be seen to articulate a midpoint on a description of a term that creates a contradictory continuum, neither positive (happy) nor negative (un- opposition.