Article
History & Philosophy Of Science
Alexander R. Pruss
Summary: Classical real-valued probabilities have philosophical costs, and three non-classical approaches have been suggested to avoid the drawbacks. However, these approaches have been criticized for failing to preserve intuitive symmetries. This paper offers technical results to explore the conditions under which these symmetries can be preserved by these non-classical probabilities.
Review
Mathematics
Hykel Hosni, Jurgen Landes
Summary: This paper illustrates the usefulness of logical methods and techniques in the foundations and applications of reasoning under uncertainty, which are currently undervalued. The field encompasses logic, artificial intelligence, statistics, and decision theory. Instead of attempting a comprehensive survey, the paper focuses on a few notable examples. While the majority of attention is given to probabilistic frameworks for quantifying uncertainty, the paper also touches upon generalizations of probability measures that have gained significant interest in recent decades.
Article
Computer Science, Software Engineering
Lola Burgueno, Paula Munoz, Robert Clariso, Jordi Cabot, Sebastien Gerard, Antonio Vallecillo
Summary: The article explores the handling of uncertain information in various domains of information systems. It focuses on representing and processing uncertain information in domain models and incorporating stakeholders' beliefs. The authors demonstrate the association of beliefs with model elements, the propagation and operation of associated uncertainty, and the individual reasoning about models enriched with personal opinions. Additionally, the article addresses the challenge of merging opinions from different domain experts and offers strategies and a methodology for optimal opinion merging.
ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY
(2023)
Article
Mechanics
Paolo Muratore-Ginanneschi, Luca Peliti
Summary: We analyze Furth's classical uncertainty relations from 1933 using modern stochastic differential equations. Our focus is on their application to non-equilibrium classical statistical mechanics. We show that Furth's uncertainty relations are inherent in martingales in diffusion processes. This implies a lower bound on the fluctuations in current velocities of entropic quantifiers in stochastic thermodynamics. Additionally, we extend Furth's relations to piecewise deterministic processes and generalize our results to general Markov processes.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2023)
Article
Computer Science, Artificial Intelligence
Norihiro Kamide
Summary: In this study, Gentzen-type sequent calculi BDm and BDi are introduced for modal extension and intuitionistic modification of extended Belnap-Dunn logic BD+ with classical negation. Theorems for embedding BDm and BDi into existing calculi for normal modal and intuitionistic logic are proven, leading to cut-elimination, decidability, and completeness theorems. Additionally, embedding theorems for BD+ into BDi and BDi into BDm are established, including Glivenko theorem and McKinsey-Tarski theorem.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Zening Zhao, Wei Duan, Guojun Cai, Meng Wu, Songyu Liu
Summary: This study develops a fully probabilistic framework for liquefaction potential evaluation, which includes an XGBoost model and the Bayesian theorem. It effectively predicts the probability of liquefaction and obtains updated parameter distributions. With comprehensive up-sampling and model validation methods, a reliable model building procedure is established, and probability contour maps and a simplified probabilistic model are provided for improved practical feasibility.
COMPUTERS AND GEOTECHNICS
(2022)
Article
Computer Science, Theory & Methods
Gonzalo E. Imaz
Summary: This paper presents research on the relevance of polynomial classes of formulas to deductive efficiency. A new class, RH, is introduced by combining regular classes: Horn and NC. It is shown that RH can be recognized and solved polynomially and it is tractable. RH is also extended to other non-classical logics and can pave the way for efficient non-clausal approximate reasoning.
FUZZY SETS AND SYSTEMS
(2023)
Article
Logic
Norihiro Kamide
Summary: In this study, an extended paradefinite logic with classical negation (EPLC) is introduced and its completeness, cut-elimination, and decidability theorems are proved. Additionally, some important properties of EPLC are shown.
LOGICA UNIVERSALIS
(2022)
Article
Engineering, Multidisciplinary
Julio C. Urenda, Olga Kosheleva, Shahnaz Shahbazova, Vladik Kreinovich
Summary: According to the research findings, in both deterministic and fuzzy cases of data processing, the distribution of uncertainty exhibits characteristics of a Gaussian distribution.
ACTA POLYTECHNICA HUNGARICA
(2022)
Article
Engineering, Ocean
Maryam Sadat Seyedpour, Ali Derakhshani
Summary: This paper analyzes the effects of uncertainty on the stability of anchored cantilever sheet pile walls in the sand using fuzzy set theory and genetic algorithm. The results show that uncertainty in different parameters has a significant impact on the wall stability, and changes in water level, anchor tensile force, and wall section modulus also affect the probability of different failure modes.
APPLIED OCEAN RESEARCH
(2023)
Article
Mathematics
J. Fernandez-Sanchez, S. Maghsoudi, D. L. Rodriguez-Vidanes, J. B. Seoane-Sepulveda
Summary: In this paper, the non-Archimedean counterpart of classical analysis in the theory of lineability is studied and new results and improvements are shown. The paper analyzes the algebraic genericity of sets of functions with properties regarding continuity, discontinuity, Lipschitzianity, differentiability, and analyticity, as well as the lineability of sets of sequences with properties concerning boundedness and convergence. The algebraic genericity of functions that do not satisfy Liouville's theorem, sequences that do not satisfy the classical theorem of Cesaro, and functionals that do not satisfy the classical Hahn-Banach theorem is also demonstrated.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Computer Science, Software Engineering
Olga Brezhneva, Yuri G. Evtushenko, Alexey A. Tret'yakov
Summary: The paper demonstrates connections between classical results of Analysis and Optimization, with a focus on providing new elementary proofs of the Implicit Function Theorem, Lusternik's Theorem, and optimality conditions for equality constrained optimization problems. These proofs rely on Fermat's Theorem and the Weierstrass Theorem, making them accessible in introductory courses without requiring an advanced background in analysis. Additionally, the paper offers a simple proof of the Implicit Function Theorem in normed linear spaces.
OPTIMIZATION METHODS & SOFTWARE
(2021)
Article
History & Philosophy Of Science
Petr Cintula, Berta Grimau, Carles Noguera, Nicholas J. J. Smith
Summary: This article discusses two degree theories on vagueness: the traditional classical theory and the fuzzy logic-based theory. The classical theory allows for rich analysis, while the fuzzy theory provides a better solution to the sorites paradox.
Article
Quantum Science & Technology
John B. DeBrota, Peter J. Love
Summary: We present a general approach to modeling rational decision-making agents based on the Quantum Bayesian approach. By introducing a scheme that allows one agent's properties to influence another, we develop a flexible framework for treating multiple interacting quantum and classical Bayesian agents. Simulations in various settings demonstrate the effectiveness of our construction, which can help interpret existing multi-agent protocols and suggest new approaches in quantum algorithm design and other areas.
Article
Engineering, Electrical & Electronic
Zhen Zhao, Peter Xiaoping Liu, Jinfeng Gao
Summary: This article presents a new fault detection scheme for stochastic distribution systems with non-Gaussian variables based on a probabilistic framework. The output probability density function (pdf) is utilized as the available information instead of the measured outputs. The proposed method utilizes the square-root B-spline function to formulate the output pdfs and develops probabilistic parameter models to capture system uncertainties and faults. An observer is designed to detect multiplicative and additive faults, and a randomized algorithm is adopted to design the threshold for achieving an optimal balance between the false alarm rate (FAR) and the fault detection rate (FDR).
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2022)
