In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, ...we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of "negation", which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.
Pre-training by language modeling has become a popular and successful approach to NLP tasks, but we have yet to understand exactly what linguistic capacities these pre-training processes confer upon ...models. In this paper we introduce a suite of diagnostics drawn from human language experiments, which allow us to ask targeted questions about information used by language models for generating predictions in context. As a case study, we apply these diagnostics to the popular BERT model, finding that it can generally distinguish good from bad completions involving shared category or role reversal, albeit with less sensitivity than humans, and it robustly retrieves noun hypernyms, but it struggles with challenging inference and role-based event prediction— and, in particular, it shows clear insensitivity to the contextual impacts of negation.
The meaning of expressions modified by double negation (e.g., not unhappy or not not interesting) has long been discussed, with views advocating that the two negations must be logically interpreted ...(i.e., not unhappy means happy), and others arguing that the modified expression always yields a weaker version than the unmodified expression. The current study aimed to understand the possible interpretations of double negation experimentally. We used a novel range-marking task, allowing (Hebrew-speaking) participants to mark not only the location of a certain expression on the scale, but also the size it occupies. We collected measures of the range sizes, their location, as well as the inclusion of the edge of the scale. Doubly-negated adjectives were compared to unmodified adjectives and singly-negated adjectives, and adjectives modified by hedges, considering their mitigation effect. We were able to provide the first empirical evidence that double negation can be interpreted both logically and pragmatically. Additionally, we showed dissimilarities between double negations and hedges, suggesting that doubly-negated expressions present a stronger mitigation effect than hedges.
•Double negation has logical and enriched interpretations.•A novel range-marking task allowed testing for the range of potential meanings.•1st Empirical evidence for multifunctionality of double negation.•Different mitigation effects for double negation and hedges.•Context may affect the range of interpretation for double negation.
We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under ...different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.
N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A ...consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing.
Questions to Michael Dunn Wansing, Heinrich; Olkhovikov, Grigory; Omori, Hitoshi
Logical Investigations,
05/2021, Volume:
27, Issue:
1
Journal Article
Peer reviewed
Open access
We present nine questions related to the concept of negation and, in passing, we refer to connections with the essays in this special issue. The questions were submitted to one of the most eminent ...logicians who contributed to the theory of negation, Prof. (Jon) Michael Dunn, but, unfortunately, Prof. Dunn was no longer able to answer them. Michael Dunn passed away on 5 April 2021, and the present special issue of Logical Investigations is dedicated to his memory. The questions concern (i) negation-related topics that have particularly interested Michael Dunn or to which he has made important contributions, (ii) some controversial aspects of the logical analysis of the concept of negation, or (iii) simply properties of negation in which we are especially interested. Though sadly and regrettably unanswered by the distinguished scholar who intended to reply, the questions remain and might stimulate answers by other logicians and further research.
Oji-Cree (Algonquian) makes use of two negation constructions which overlap in non-future environments and differ subtly in their pragmatic contexts of use. Ci-negation is used for neutral, ...descriptive negation whereas hsii-negation is associated with polemic, emphatic-like uses within stronger assertions. While hsii-negation dates to Proto-Ojibwe, I show that ci-negation developed more recently from indirect irrealis expressions as a way to downplay the inherent abruptness of negation. This represents an opposite pathway from Jespersen’s Cycle, which is partly motivated by the desire to emphasize negatives. Oji-Cree ci-negation instead arose as a new unemphatic expression, motivated by the desire to avoid social tension. Though many languages of the world feature multiple standard negation constructions, the development of these systems remain to be investigated in relation to their diachrony and social contexts. This study contributes to our knowledge of why and how such systems might arise
On the Negation of discrete Z-numbers Liu, Qing; Cui, Huizi; Tian, Ye ...
Information sciences,
October 2020, 2020-10-00, Volume:
537
Journal Article
Peer reviewed
The negation of a problem provides a new perspective for information representation. However, existing negation method has limitations since it can only be applied to the accurately expressed ...knowledge. Real-world information is imperfect and imprecise. It usually describes in natural language. In view of this, Prof. Zadeh suggested the concept of Z-number as a more adequate way for description of real world information. As Z-number involves both fuzzy and probabilistic uncertainty, a novel method for the negation of Z-number in combination of probability and fuzziness is proposed from the reliability of probability transmission in this paper. Moreover, several examples are used to describe the negation process and result. As far as our latest knowledge is concerned, the negation of Z-number has not been covered by researchers, so this may be another door for us to process Z-number-based information.
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