Conversational Negation using Worldly Context in Compositional Distributional Semantics (2021)

Abstract: We propose a framework to model an operational conversational negation by applying worldly context (prior knowledge) to logical negation in compositional distributional semantics. Given a word, our framework can create its negation that is similar to how humans perceive negation. The framework corrects logical negation to weight meanings closer in the entailment hierarchy more than meanings further apart. The proposed framework is flexible to accommodate different choices of logical negations, compositions, and worldly context generation. In particular, we propose and motivate a new logical negation using matrix inverse. We validate the sensibility of our conversational negation framework by performing experiments, leveraging density matrices to encode graded entailment information. We conclude that the combination of subtraction negation and phaser in the basis of the negated word yields the highest Pearson correlation of 0.635 with human ratings.

## introduction negation is fundamental to every human language, marking a key difference from how other animals communicate @xcite . it enables us to express denial, contradiction, and other uniquely human aspects of language. as humans, we know that negation has an operational interpretation: if we know the meaning of a, we can infer the meaning of not a, without needing to see or hear not a explicitly in any context. formalizing an operational description of how humans interpret negation in natural language is a challenge of significance to the fields of linguistics, epistemology, and psychology. @xcite notes that there is no straightforward negation operation that, when applied to the distributional semantics vector of a word, derives a negation of that word that captures our intuition. this work proposes and experimentally validates an operational framework for conversational negation in compositional distributional semantics. in the field of distributional semantics, there have been developments in capturing the purely logical form of negation. @xcite introduce the idea of computing negation by mapping a vector to its orthogonal subspace; @xcite analogously model their logical negation for density matrices. however, logical negation alone is insufficient in expressing the nuances of negation in human language. consider the sentences: a) this is not an apple; this is an orange. b) this is not an apple; this is a paper. sentence a) is more plausible in real life than sentence b). however, since apples and oranges share a lot in common, their vector or density matrix encodings would most likely not be orthogonal. consequently, such a logical negation of apple would more likely indicate a paper than an orange. @xcite propose that the encoding of a word should have a distinct "domain" and "value", and its negation should only affect the "value". in this way, not blue would still be in the domain of color. however, they do not provide any scalable way to generate such representation of "domain" and "value" from a corpus. we argue that this domain need not be encoded in the vector or density matrix itself. instead, we propose a method to generate what we call worldly context directly from the word and its relationships to other words, computed a priori using worldly knowledge. furthermore, we want such conversational negation to generalize from words to sentences and to entire texts. discocat @xcite provides a method to compose the meaning of words to get the meaning of sentences and discocirc (coecke, 2020) extends this to propagate knowledge throughout the text. therefore, we propose our conversational negation in the discocirc formalism, putting our framework in a rich expanse of grammatical types and sentence structures. focusing on the conversational negation of single words, we leave the interaction of conversational negation with grammatical structures for future work. section 2 introduces the necessary background. section 3 discusses the logical negation using subtraction from the identity matrix from lewis (2020), and proposes and justifies a second, new form of logical negation using matrix inverse. section 4 introduces methods for context creation based on worldly knowledge. section 5 presents the general framework for performing conversational negation of a word by combining logical negation with worldly context. section 6 experimentally verifies the proposed framework, comparing each combination of different logical negations, compositions, bases, and worldly context generation. we end our discussion with an overview of future work. @xcite point out a long tradition in formal semantics, pragmatics and psycholinguistics which has argued that negation-in human conversation-is not simply a denial of information; it also indicates the truth of an alternative assertion. they call this alternative-licensing view of negation conversational negation. ## logical negations to construct conversational negation, we must first define a key ingredient -logical negation, denoted by ¬. the logical negation of a density matrix is a unary function that yields another density matrix. the most important property of a logical negation is that it must interact well with hyponymy. ideally, the interpretation of the contrapositive of an entailment must be sensible: a weakened notion arises from allowing varying degrees of entailment: we now discuss two candidates for logical negation that have desirable properties and interaction with the hyponymies presented in section 2.4. ## experiments to validate the proposed framework, we perform experiments on the data set of alternative plausibility ratings created by @xcite foot_0 . in their paper, @xcite predict plausibility scores for word pairs consisting of a negated word and its alternative using various methods to compare the similarity of the words. while achieving a high correlation with human intuition, they do not provide an operation to model the outcome of a conversational negation. through the experiments, we test whether our operational conversational negation still has correlation with human intuition. ## future work the framework presented in this paper shows promising results for conversational negation in compositional distributional semantics. given its modular design, additional work should be done exploring more kinds of logical negations, compositions and worldly contexts, as well as situations for which certain combinations are optimal. since creating worldly context-as presented in this paper-is a new concept in the area of disco-circ, it leaves the most room for further exploration. in particular, our framework does not handle how to disambiguate different meanings of the same word; for example, the worldly context of the word apple should be different for the fruit apple versus the technology company apple. our conversational negation framework currently does not model a different kind of negation where the suggested alternative is an antonym rather than just any other word that appears in similar contexts. for instance, the sentence alice is not happy suggests that alice is sad-an antonym of happy-rather than cheerful, even though cheerful might appear in similar contexts as happy. we would like to extend the conversational negation framework to account for this. we would like to implement the context generation method presented in section 4.1.2 and test on the current experimental setup. 2 to further validate the framework, more data sets should be collected and evaluated on to explore, for each type of relation between words, what construction of conversational negation yields sensible plausibility ratings. for the conversational negation to be fully applicable in the context of compositional distributional semantics, further theoretical work is required to generalize the model from negation of individual nouns to negation of other grammatical classes and complex sentences. furthermore, we would like to analyze the interplay between conversational negation, textual context, and evolving meanings. lastly, the interaction of conversational negation with logical connectives and quantifiers leaves open questions to explore.