The entropy of Łukasiewicz-languages

The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language

Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200

Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications

In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a multiplicative constant. We then apply a natural process "simulate-guess-and-proof" to analyze the height of a random Motzkin in function of its frequency of unary nodes. When the number of unary nodes dominates, we prove some unconventional height phenomenon (i.e. outside the universal square root behaviour.)Comment: 19 page

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Ontology-Mediated Query Answering over Log-Linear Probabilistic Data: Extended Version

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results

Fuzzy expert systems in civil engineering

Imperial Users onl

CoAnnotating: Uncertainty-Guided Work Allocation between Human and Large Language Models for Data Annotation

Annotated data plays a critical role in Natural Language Processing (NLP) in training models and evaluating their performance. Given recent developments in Large Language Models (LLMs), models such as ChatGPT demonstrate zero-shot capability on many text-annotation tasks, comparable with or even exceeding human annotators. Such LLMs can serve as alternatives for manual annotation, due to lower costs and higher scalability. However, limited work has leveraged LLMs as complementary annotators, nor explored how annotation work is best allocated among humans and LLMs to achieve both quality and cost objectives. We propose CoAnnotating, a novel paradigm for Human-LLM co-annotation of unstructured texts at scale. Under this framework, we utilize uncertainty to estimate LLMs' annotation capability. Our empirical study shows CoAnnotating to be an effective means to allocate work from results on different datasets, with up to 21% performance improvement over random baseline. For code implementation, see https://github.com/SALT-NLP/CoAnnotating