Degree Of Truth Research Articles

Cut-free sequent-style systems for a logic associated to involutive Stone algebras

Abstract In [4, 5], it was introduced a logic (called Six) associated to a class of algebraic structures known as involutive Stone algebras. This class of algebras, denoted by S, was considered by the first time in [6] as a tool for the study of certain problems connected to the theory of finite-valued Łukasiewicz–Moisil algebras. In fact, Six is the logic that preserves degrees of truth with respect to the class S. Among other things, it was proved that Six is a 6-valued logic that is a Logic of Formal Inconsistency (LFI ); moreover, it is possible to define a consistency operator in terms of the original set of connectives. A Gentzen-style system (which does not enjoy the cut-elimination property) for Six was given. Besides, in [5], it was shown that Six is matrix logic that is determined by a finite number of matrices; more precisely, four matrices. However, this result was further sharpened in [17], proving that just one of these four matrices determine Six, i.e. Six can be determined by a single 6-element logic matrix. In this work, taking advantage of this last result, we apply a method due to Avron, Ben-Naim and Konikowska [3] to present different Gentzen systems for Six enjoying the cut-elimination property. This allows us to draw some conclusions about the method as well as to propose additional tools for the streamlining process. Finally, we present a decision procedure for Six based in one of these systems.

Bousi[formula omitted]Prolog: Design and implementation of a proximity-based fuzzy logic programming language

The fuzzy logic programming language Bousi∼Prolog extends Prolog with a weak unification algorithm based on proximity relations and truth degree annotations. The weak unification algorithm makes the search for answers more flexible, while rule annotations make possible knowledge-based applications where the rules may be uncertain. In this paper, after recalling the main concepts supporting this language, we detail its design and implementation. We describe the implementation of its operational semantics, which is based on compiling programs and queries into Prolog, and those important features that makes it more applicable: fuzzy sets, integration with WordNet and efficiency techniques. The result is a high-level open-source implementation of the Bousi∼Prolog system, written on top of SWI-Prolog, and publicly available. We also summarise some experiments measuring its performance compared to other systems.

A fairness-concern-based LINMAP method for heterogeneous multi-criteria group decision making with hesitant fuzzy linguistic truth degrees

Heterogeneous multi-criteria group decision making (MCGDM) is a hot topic in the decision analysis field. This paper proposes a fairness-concern-based LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method for heterogeneous MCGDM with hesitant fuzzy linguistic (HFL) truth degrees. Heterogeneous evaluation information includes crisp numbers, interval numbers, intuitionistic fuzzy values (IFVs), trapezoidal fuzzy numbers (TrFNs) and hesitant fuzzy sets (HFSs). This paper introduces the fairness concern to calculate the HFL consistency and the HFL inconsistency indices. Based on the framework of LINMAP, a bi-objective HFL programming model is built to derive the criteria weights, the positive ideal fairness vector (PIFV) and the negative ideal fairness vector (NIFV) for each decision maker (DM) simultaneously. Based on the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), a multi-objective programming model is built to obtain DMs’ weights. The alternatives ranking is derived by comprehensive collective relative closeness degrees. Finally, a real example is applied to verify effectiveness and superiority of this heterogeneous MCGDM method. The proposed heterogeneous MCGDM method provides a very useful approach for MCGDM with heterogeneous information.

Rational Pavelka logic: The best among three worlds?

This comparative survey explores three formal approaches to reasoning with partly true statements and degrees of truth, within the family of Łukasiewicz logic. These approaches are represented by infinite-valued Łukasiewicz logic (Ł), Rational Pavelka logic (RPL) and a logic with graded formulas that we refer to as Graded Rational Pavelka logic (GRPL). Truth constants for all rationals between 0 and 1 are used as a technical means to represent degrees of truth. Łukasiewicz logic ostensibly features no truth constants except 0 and 1; Rational Pavelka logic includes constants in the basic language, with suitable axioms; Graded Rational Pavelka logic works with graded formulas and proofs, following the original intent of Pavelka, inspired by Goguen's work. Historically, Pavelka's papers precede the definition of GRPL, which in turn precedes RPL; retrieving these steps, we discuss how these formal systems naturally evolve from each other, and we also recall how this process has been a somewhat contentious issue in the realm of Łukasiewicz logic. This work can also be read as a case study in logics, their fragments, and the relationship of the fragments to a logic.

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Previous article FreeBack CoverPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreThe Price of FalsehoodsJames Fisk, Jr., was still more original in character. He was not yet forty years of age, and had the instincts of fourteen. He came originally from Vermont, probably the most respectable and correct State in the Union, and his father had been a pedler who sold goods from town to town in his native valley of the Connecticut. The son followed his father’s calling with boldness and success. He drove his huge wagon, made resplendent with paint and varnish, with four or six horses, through the towns of Vermont and Western Massachusetts; and when his father remonstrated at his reckless management, the young man, with his usual bravado, took his father into his service at a fixed salary, with the warning that he was not to put on airs on the strength of his new dignity…..Personally Fisk was coarse, noisy, boastful, ignorant, the type of a young butcher in appearance and mind…. A story not without a stroke of satirical wit was told by him to illustrate his estimate of abstract truth. An old woman who had bought of the elder Fisk a handkerchief which cost ninepence in the New England currency, where six shillings are reckoned to the dollar, complained to Mr. Fisk, Jr., that his father had cheated her. Mr. Fisk considered the case maturely, and gave a decision based on a priori principles. “No!” said he, “the old man would n’t have told a lie for ninepence;” and then, as if this assertion needed some reasonable qualification, he added, “though he would have told eight of them for a dollar!” The distinction as regarded the father may have been just, since the father held oldfashioned ideas as to wholesale and retail trade; but in regard to the son this relative degree of truth cannot be predicated with confidence, since, if the investigating committee of Congress and its evidence are to be believed, Mr. Fisk seldom or never speaks truth at all.[Henry Adams, Historical Essays (London: T. Fisher Unwin, 1891), 323–25]Originally featured on the December 1989 (vol. 97, no. 6) back cover Previous article DetailsFiguresReferencesCited by Journal of Political Economy Volume 130, Number 8August 2022 Article DOIhttps://doi.org/10.1086/721829 Views: 208Total views on this site © 2022 The University of Chicago. All rights reserved.PDF download Crossref reports no articles citing this article.

Graded Many-Valued Modal Logic and Its Graded Rough Truth

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by employing the graded operators that correspond to graded modal operations in G(S5), we introduce the concept of graded upper and lower rough truth degrees of a logical formula. Then, we propose the graded upper and lower conditional rough truth degrees. Several basic interesting properties are addressed. Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established in a very natural way.

Not Half True

AbstractThe word ‘true’ shows some evidence of gradability. For instance, there are cases where truth-bearers are described as ‘slightly true’, ‘completely true’ or ‘very true’. Expressions that accept these types of modifiers are analysed in terms of properties that can be possessed to a greater or lesser degree. If ‘true’ is genuinely gradable, then it would follow that there are degrees of truth. It might also follow that ‘true’ is context-sensitive, like other gradable expressions. Such conclusions are difficult to reconcile with most existing theories: deflationists and inflationists alike tend to reject the thesis that one true truth-bearer can have more or less truth than another. Based on work in natural language, I argue that ‘true’ is not a genuinely gradable expression. I also provide an explanation of the apparent evidence for gradability. Hence there is no reason to think that there is a truth property that comes in degrees.

Expanding Belnap 2: the dual category in depth

Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N.D. Belnap in a 1977 paper entitled How a computer should think. Prioritised default bilattices include not only Belnap’s four values, for ‘true’ (t), ‘false’(f), ‘contradiction’(⊤) and ‘no information’ (⊥), but also indexed families of default values for simultaneously modelling degrees of knowledge and truth. Prioritised default bilattices have applications in a number of areas including artificial intelligence. In our companion paper, we introduced a new family of prioritised default bilattices, Jn, for n ⩾ 0, with J0 being Belnap’s seminal example. We gave a duality for the variety Vn generated by Jn, with the dual category Xn consisting of multi-sorted topological structures. Here we study the dual category in depth. We axiomatise the category Xn and show that it is isomorphic to a category Yn of single-sorted topological structures. The objects of Yn are ranked Priestley spaces endowed with a continuous retraction. We show how to construct the Priestley dual of the underlying bounded distributive lattice of an algebra in Vn via its dual in Yn; as an application we show that the size of the free algebra FVn(1) is given by a polynomial in n of degree 6.

Group conflict handling under moderate evaluative partial mediation using entropic decision framework

AbstractThe present paper aims to present entropy and fuzzy degrees of the truth‐based framework to handle the group conflict under moderate evaluative, partial mediation. For group conflict handling, the present work considers Thomas and Kilmann's five conflict‐handling modes: competing, collaborating, avoiding, accommodating, and compromising. A methodology proposed in the current work systemically formalizes decision‐making on deploying a conflict‐handling method with mediators' opinions. The formalization of decision‐making elucidated in the present work involves measurements based on entropy and fuzzy degrees of truth. The current work applies the developed formal quantitative framework to a well‐known case of group conflict that involves conflict among a group of engineering students. The case supports the proposed formal framework. Behavioral, psychological, and cognitive facts about engineers come in handy for validation of the proposed framework. The case shows that the proposed approach can be highly generalized, interpretable, and replicable.

New multi-criteria decision-making technique based on neutrosophic axiomatic design

There are several multicriteria decision-making (MCDM) approaches presented in the literature with their characteristics. Although traditional MCDM approaches are considered a proper implementation to select the best alternative from available types, they failed to consider uncertainty which is quite high and desires to be thoughtfully measured in the selection process. This research focuses on extending MCDM in the neutrosophic environment using axiomatic design (AD) as a novel contribution to selecting appropriate Computed Tomography (CT) devices. We present a new linguistic scale for evaluating criteria and alternatives based on single-valued triangular neutrosophic numbers (SVTrN). The proposed approach is superior to other existing approaches due to its simplicity and ability to simulate natural human thinking via considering truth, indeterminacy, and falsity degrees. Then, applying it will increase the value of imaging for medical decision-making and decrease needless costs. So, this study can be valuable to researchers by helping them consider the appropriate medical imaging system selection problem theoretically under uncertainty, and for governments and organizations to design better satisfying medical imaging evaluation systems.

Heterogeneous formal context and its decomposition by heterogeneous fuzzy subsets

Fuzzy relations are the mappings which are intensively studied in decision, reasoning, or data analysis. We propose a method for decomposition of heterogeneous formal context by heterogeneous fuzzy subsets, which allows representing the heterogeneous structure of truth degrees for each object, heterogeneous structure of truth degrees for each attribute and heterogeneous structure of truth degrees for relationship between each pair of object and attribute. We formulate and prove the properties of decomposition in heterogeneous extension of Formal concept analysis. We put emphasis on the role of special heterogeneous formal concepts which are generated from heterogeneous singleton fuzzy subsets. We illustrate our novel results in our running example of personal requirements for accommodation as the natural continuation of our previous studies.

A synergy-effect-incorporated fuzzy Petri net modeling paradigm with application in risk assessment

As a graphical knowledge representation and reasoning tool, fuzzy Petri net (FPN) is widely used in risk assessment, fault diagnosis and many other fields. It can express the complex causal relationships among events and make fuzzy reasoning about them. In practical applications, there may be synergy effects among events, i.e., the occurrence of event a may increase or decrease the truth degree of event b. Traditional FPNs fail to express such effects, thus neglecting them during their reasoning procedure. To address this issue, this study proposes an FPN considering them for the first time. Firstly, this study illustrates the concept of synergy effects via practical application examples. Secondly, it develops the transition enabling conditions and truth degree calculation rules incorporated with synergy effects. Then, it formally defines a synergy-effect-incorporated fuzzy Petri net (SFPN). On this basis, it presents the production rules, transition firing rules and reasoning algorithm of SFPN to perform knowledge representation and reasoning for knowledge-based systems affected by synergy effects. Finally, it takes the risk assessment of equipment failure caused by corrosion as a running case to validate its feasibility and advantages.

From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic

We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.

On neutro-Hv-semigroups

In this paper, we extend the notion of Hv-semigroups to neutro-Hv-semigroups and anti-Hv-semigroups and investigate many of their properties. We show that these new concepts are different from the classical concept of Hv-semigroups by presenting several examples. In general, the neutro-algebras and anti-algebras are generalizations and alternatives of classical algebras. The goal and benefits of our proposed extension of this study is to explore not only the hyperoperations and axioms that are totally true as in previous algebraic hyperstructures, but also the cases when they have degrees of truth, indeterminacy and falsehood. Therefore, we enlarge the field of research.

SaltISCG: Interactive Salt Segmentation Method Based on CNN and Graph Cut

Salt body extraction plays an important role in the analysis of salt structures and the exploration of oil and gas. Seismic attributes and edge detection algorithms, which require manual effort, are the conventional methods of extracting salt boundaries from seismic images. Convolutional neural networks (CNNs) have become the state-of-the-art automatic segmentation method for seismic interpretation. However, the fully automatic results of the extraction of salt boundaries may still need to be modified to become accurate and robust enough for practical production. We present a novel deep-learning-based interactive segmentation method for extracting salt boundaries. To incorporate the interaction points into our method, we transform positive and negative points into two Euclidean distance maps (EDMs), which are combined with seismic images to train our CNN model. The model is composed of a U-net and a pyramid pooling module, and it is trained on the TGS Salt Identification Challenge dataset. Then, we use a graph cut algorithm to refine the likelihood maps predicted by our CNN model and subsequently update the salt boundaries. Some field examples show that the proposed method outperforms fully automatic CNN methods with a higher matching degree of the ground truth.

Trends summarization of times series: a multi-objective genetic algorithm-based model

Aim: The explosion of the amounts of data generated in many application domains, makes the paradigm of data summarization more essential. Furthermore, it is of a great interest to effectively handle some specific needs. In this work, we discuss an advanced model to drive linguistic summarization in the context of time series. This model relies on a multi-objective genetic algorithm mechanism to generate a set of best summaries from a large number of candidates. Methods: To achieve this objective, the current work is divided into two parts: The first part is dedicated for extracting the linguistic summaries of the dynamic characteristics of the trends of time series. It is achieved using the traditional genetic algorithm where the fitness function represents the truth degree of the linguistic quantified proposition. The second part is devoted to formalise the problem of interest as a multi-criteria optimization problem. We use different quality measures of summary as targets for improving the predicted set of summaries. To reach this goal, we use the Fast Non-Dominated Sorting Genetic Algorithm NSGA-II. Results: We evaluate the proposed approach on real data from a Smart Campus application (Neocampus project of the University of Toulouse, France). The results are promising and confirming the usability of the proposed approach. Conclusion: The proposed approach overcomes the problem of the overabundance of irrelevant linguistic summaries of the time series. It allows selecting a set of best summaries regarding some relevant criteria.

A novel hybrid method of lithology identification based on k-means++ algorithm and fuzzy decision tree

Lithology identification methods based on conventional logging data are essential in reservoir geological evaluation. Due to the highly non-linear relationship between lithology and various logging parameters, conventional methods cannot meet the requirements. In recent years, machine learning methods such as Neural Networks and decision tree have been applied to the field of lithology identification and achieved good effects. However, there is no obvious difference in logging parameters for various types of lithology, and at the same time, there is a large amount of information redundancy between each logging curve. Therefore, its uncertainty and fuzziness are high, which interferes with the result of lithology identification. Combining fuzzy theory, decision tree and K-means++ algorithm, this paper proposes a novel hybrid technique of lithology identification which can better overcome the ambiguity and uncertainty of logging data. In the actual data test, we select six logging parameters: density (RHOB), neutron porosity (NPHI), natural gamma (GR), longitudinal wave velocity (VP), shallow formation resistivity (LLS), and deep formation resistivity (LLD). Then K-means++ clustering algorithm was used for clustering analysis on logging data. Finally, the triangular membership function is selected to fuzz the logging data according to the obtained clustering center points, and a fuzzy decision tree lithology identification model is constructed. The prediction accuracy of the model reached 93.92%. The fuzzy decision tree algorithm was also compared with five machine learning algorithms, including decision tree, extremely randomized trees (ET), Adaboost, random forest (RF) and gradient boosting decision tree (GBDT). The results show that the modeling results of fuzzy decision tree algorithm outperform other algorithms. In summary, the fuzzy decision tree model developed in the study is a practical and effective model for complex lithology identification, providing a new idea for lithology identification. • A fuzzy decision tree model using logging data for lithology identification is proposed. • The k-means++ algorithm optimizes the selection of initial clustering centers. • Logging data is fuzzily processed by the triangular membership function. • Pre-pruning the fuzzy decision tree by controlling the values of significance level α and truth degree threshold β. • The accuracy of the model can reach 93.92%, which is better than other algorithms.

Konstruksi Epistemologi Islam (Studi Komparasi Konsep Mushawwibah dan Mukhaththiah dalam Ushul Fiqh)

Fast traslate Icon translate In this paper the author tries to explore how the construction of Islamic epistemology, through a study in the field of fiqh and fiqh proposals regarding the theory of Mushawwibah and Mukhaththiah in Ushul Fiqh. An understanding of this issue is very important, considering that currently there are so many groups calling for the need for knowledge in the field of fiqh and proposals of fiqh due to the overflowing invasion of Western social sciences. We are required not to rush to reject new ones and also not to leave the treasures of classical Islamic scholarship, before understanding them properly and correctly with the Mushawwibah and Mukhaththiah Theory in this Ushul Fiqh. Ushul Fqh is better able to enter the sides of legal issues related to the behavior of Muslims. So that for followers of the Mushawwibah theory it is explained that all the different conclusions, which are not one true, may even be all true. That is if all the mujtahids present a frame of mind that is in line with the ushul-fiqh path. Meanwhile, followers of mukhaththiah argue that all the many conclusions are correct, only one, especially if some of these conclusions have contradictory values. This research found that Islam studies all texts both implied in the Koran and al-Hadith, both in the form of zhanni (allegations), thus the meaning that emerges from the text is always formulated in different conclusions, meaning that it is still mukhtalaf fih or dissent. In the study offered by the Mushawwibah theory, it is explained that all the different conclusions, which are not one, may even be all true. This is the case if the mujtahids present a frame of mind that is in line with the rules of ushul-fiqh. In contrast to the mukhaththiah theory which argues that all the many conclusions mentioned earlier, only one is correct, this is because if several conclusions exist have contradictory values. Such judgments arise because ushul fiqh or fiqh thinking framework makes use of subjective reasoning and qualitative paradigms. This type of reasoning lacks some degree of truth. The truth of ushul fiqh is considered contrived and its true nature is speculative.

Pengaruh Penerapan Pembelajaran Kooperatif Tipe Pair Checks Terhadap Hasil Belajar Matematika Siswa Kelas VIII SMP Pertiwi 2 Padang

The background of this research is that srudents’ mathematics learning outcomes are still low, students participate less and have not maximized their role in group learning. The purpose of the study was to determine the improvement of students’ mathematics learning outcomes by applying the pair checks type cooperative learning model to the VIII grade students of SMP Pertiwi 2. This type of researchis pre-experimental design research with research design one shoot case study. The population in this study were students class VIII SMP Pertiwi 2 Padang which consists of 2 classes retrieval technique. The sample was taken using purposive sampling, so that class VIII.1 was chosen SMP Pertiwi 2 Padang as a sample. The research instrument is the final test in the form of essays and reliability of questions = 0,86 with reliable criteria. Based on the calculation results, it was obtained that the percentage of learning outcomes obtained by students while using the pair checks type of cooperative learning model obtained t count = -2,5 = 2,5 (absolute value) and t table = 1,79 with the degree of truth (dk) = n-1, n = 12 then (dk) = 11 and a significant rate of 5% = 0,05. So is rejected because t count > t table. So it can be concluded that there is an increase in student learning outcomes by applying the pair checks cooperative learning model to class VIII students SMP Pertiwi 2 Padang.

Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making

The hesitant fuzzy 2-dimension linguistic element (HF2DLE) allows decision makers to express the importance or reliability of each term included in a hesitant fuzzy linguistic element as a linguistic term. This paper investigates a programming technique for multidimensional analysis of preference for hesitant fuzzy 2-dimension linguistic multicriteria group decision making. Considering the flexibility of HF2DLEs in expressing hesitant qualitative preference information, we first adopt HF2DLEs to depict both the evaluation values of alternatives and the truth degrees of alternative comparisons. To calculate the relative closeness degrees (RCDs) of alternatives, the Euclidean distances between HF2DLEs are defined. Based on RCDs and preference relations on alternatives, the group consistency and inconsistency indices are constructed, and a bi-objective hesitant fuzzy 2-dimension linguistic programming model is established to derive the criteria weights and positive and negative ideal solutions. Since the objective functions and partial constraint coefficients of the established model are HF2DLEs, an effective solution is developed, through which the RCDs can be calculated to obtain the individual rankings of alternatives. Furthermore, a single-objective assignment model is constructed to determine the best alternative. Finally, a case study is conducted to illustrate the feasibility of the proposed method, and its effectiveness is demonstrated by comparison analyses.