Fuzzy Natural Logic Research Articles

Intelligent Task Planning System Based on Methods of Fuzzy Natural Logic

In this paper, we present a novel approach to task planning based on an intelligent expert system that makes it possible to obtain a conclusion based on linguistically characterized knowledge. The main goal of the proposed task planning system is to arrange and display tasks for the solver in an effective way. Therefore, the system shows the most important tasks first and then the less important ones (in a determined ordering). The solver has a list of tasks arranged according to their importance at each time the task list is displayed. Another goal of the system is to show the effectiveness of all subordinate workers (solvers) for the manager. The expert knowledge contained in the system is characterized by three linguistic descriptions: determination of the task importance, determination of the final task importance, and determination of the efficiency of the task solvers. The system shows the ordered task list in real time. Evaluation of the relative and final importance of the tasks is performed periodically. The system has been implemented as a WEB application and verified on real data set. We also present experimental results of our system.

Fuzzy Property Grammars for Gradience in Natural Language

This paper introduces a new grammatical framework, Fuzzy Property Grammars (FPGr). This is a model based on Property Grammars and Fuzzy Natural Logic. Such grammatical framework is constraint-based and provides a new way to formally characterize gradience by representing grammaticality degrees regarding linguistic competence (without involving speakers judgments). The paper provides a formal-logical characterization of FPGr. A test of the framework is presented by implementing an FPGr for Spanish. FPGr is a formal theory that may serve linguists, computing scientists, and mathematicians since it can capture infinite grammatical structures within the variability of a language.

A Combination of Fuzzy Techniques and Chow Test to Detect Structural Breaks in Time Series

In a series of papers, we suggested a non-statistical method for the detection of structural breaks in a time series. It is based on the applications of special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). In this paper, we combine our method with the principles of the classical Chow test, which is a well-known statistical method for testing the presence of a structural break. The idea is to construct testing statistics similar to that of the Chow test which is formed from components of the first-degree F-transform. These components contain an estimation of the average values of the tangents (slopes) of the time series over an imprecisely specified time interval. In this paper, we illustrate our method and its statistical test on a real-time series and compare it with three classical statistical methods.

Exploring the complexity of natural languages: A fuzzy evaluative perspective on Greenberg universals

<abstract><p>In this paper, we introduced a fuzzy model for calculating complexity based on universality, aiming to measure the complexity of natural languages in terms of the degree of universality exhibited in their rules. We validated the model by conducting experiments on a corpus of 143 languages obtained from Universal Dependencies 2.11. To formalize the linguistic universals proposed by Greenberg, we employed the Grew tool to convert them into a formal rule representation. This formalization enables the verification of universals within the corpus. By analyzing the corpus, we extracted the occurrences of each universal in different languages. The obtained results were used to define a fuzzy model that quantifies the degree of universality and complexity of both the Greenberg universals and the languages themselves, employing the mathematical theory of evaluative expressions from fuzzy natural logic (FNL). Our analysis revealed an inversely proportional relationship between the degree of universality and the level of complexity observed in the languages. The implications of our findings extended to various applications in the theoretical analysis and computational treatment of languages. In addition, the proposed model offered insights into the nature of language complexity, providing a valuable framework for further research and exploration.</p></abstract>

Preface to the Special Issue on “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”

In [1], we gave reasons to focus on one of the possible future directions of fuzzylogic towards the concept of fuzzy natural logic (FNL). [...]

Describing Linguistic Vagueness of Evaluative Expressions Using Fuzzy Natural Logic and Linguistic Constraints

In recent years, the study of evaluative linguistic expressions has crossed the field of theoretical linguistics and has aroused interest in very different research areas such as artificial intelligence, psychology or cognitive linguistics. The interest in this type of expressions may be due to its relevance in applications such as opinion mining or sentiment analysis. This paper brings together Fuzzy Natural Logic and Fuzzy Property Grammars to approach evaluative expressions. Our contribution includes the marriage of mathematical and linguistic methods for providing a formalism to deal with the linguistic vagueness of evaluative expressions by describing the syntax and semantics of these structures. We contribute to the study of evaluative linguistic expressions by proposing a formal characterization of them where the concepts of semantic prime, borderline evaluative expressions and markedness are defined and where the relation between the semantic constraints of evaluations and their sentiment can be established. A proof-of-concept of how to create a lexicon of evaluative expressions for future computational applications is presented. The results demonstrate that linguistic evaluative expressions are gradient, have sentiment, and that the evaluations work as a relation of hypernym and hyponym, the hypernym being a semantic prime. Our findings provide the basis for building an ontology of evaluative expressions for future computational applications.

Quarterly sales analysis using linguistic fuzzy logic with weather data

Reliable estimation of customer demand for products and services constitutes a key aspect of financial planning in every company. When estimating future sales, as a proxy to demand, in addition to pure economic quantities, a large selection of (exogenous) variables specific to a given product can be considered. Potential impact of weather conditions on sales has been known for very long time, though the research using weather data has been mostly focused on energy sector. As concerns retail, several authors have started to analyze this issue only recently. This paper proposes a novel approach studying (quarterly) sales using weather data and is inspired by fuzzy natural logic. The method is based on modeling the influence of average temperatures on sales by fuzzy linguistic IF-THEN rules. The proposed methodology is applied to real data of quarterly ice-cream sales and compared with a standard approach. The results are promising especially when monthly average temperatures are considered.

Graded Structures of Opposition in Fuzzy Natural Logic

The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanche’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such as “most”, “many”, “a few”, and “almost all”, and they correspond to what are often called “fuzzy quantifiers” in the literature. The graded Peterson’s cube of opposition, which describes properties between two graded squares, will be discussed at the end of this paper.

The theory of intermediate quantifiers in fuzzy natural logic revisited and the model of “Many”

The fuzzy natural logic (FNL) is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language. One of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones. In our previous papers, we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary, contradictory, subcontrary, and subalterns between these quantifiers. Based on these relations and following Peterson's book [62], we were able to suggest a formal model of the 5-square of opposition with intermediate quantifiers. This paper picks up the threads of this work and has the following goals: it contributes to the development of the theory of fuzzy natural logic. First, it gets back to some concepts of the theory of evaluative linguistic expressions, introduces slight modifications, and proves some not yet presented properties. Furthermore, it improves the formal theory of intermediate quantifiers; some definitions are made more precise, and some new theorems are proved. Finally, it contributes to the theory of the intermediate quantifier “Many” and the analysis of its position in the mentioned 5-square. We will show that “Many” manifests an ambiguous relation towards the other quantifiers.

Forecasting seasonal time series based on fuzzy techniques

This paper is devoted to a method for the forecasting of seasonal time series. The core of our approach is based on the fuzzy transform and fuzzy natural logic (FNL) techniques. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and an irregular fluctuation, the forecasting is a combination of individual forecasting of each of these constituents. More precisely, the trend-cycle and the seasonal component are predicted with the help of fuzzy transform, pattern recognition and fuzzy natural logic techniques. To model the irregular component, we apply the Box–Jenkins approach. In the paper, we compare the suggested method with two other well-known methods, namely STL (see [14]) and ARIMA ones.

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

The paper aims at applying fuzzy natural logic together with the Fuzzy GUHA method to analyse and linguistically characterise scientific data. Fuzzy GUHA is a tool for extracting linguistic association rules from data. Obtained associations are IF-THEN rules composed of evaluative linguistic expressions, which allow the quantities to be characterized with vague linguistic terms such as very small, big, medium etc. Originally, fuzzy GUHA provides several numerical indices of rule quality, which may not be easily understandable for domain experts that are not familiar with GUHA association rules. Therefore, we show in this paper that the theory of intermediate quantifiers (a constituent of fuzzy natural logic) can be applied to the results in an automatic manner in order to obtain natural linguistic summarization. We also present an idea of how the theory of generalized Aristotles's syllogisms can be used for a detailed data analysis. We also open the possibility to use fuzzy partial logic for cases where some data is missing or undefined.

Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic (FNL). We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

Intermediate Syllogisms in Fuzzy Natural Logic

The goal of this paper is twofold: first, we give overview of the results of one part of the Fuzzy Natural Logic - the formal theory of intermediate quantifiers and syllogisms based on them. We present 105 valid basic syllogisms and show that for the proof of validity of all of them, we need to prove validity of only few of them so that validity of the other ones immediately follows. In the second part of the paper, we focused on conditions under which non-trivial intermediate syllogisms are valid. The latter are syllogisms which contain two or even three general intermediate quantifiers (not equal to any of $\forall$ or $\exists$).

Linguistic characterization of time series

The goal of this paper is to provide an overview of applications of special soft computing theories — the fuzzy transform and fuzzy natural logic — to analysis, forecasting and mining information from time series. The focus is especially placed on the ability of methods of fuzzy natural logic to provide information in sentences of natural language. Our approach is based on the decomposition of time series into three components: the trend-cycle, seasonal component and noise. The trend-cycle is extracted using the F-transform, and its course is characterized by automatically generated linguistic description. The latter is then used to forecast the trend-cycle. The trend-cycle can be, furthermore, decomposed into trend (general tendency) and cycle. The former is computed again using the F-transform. Moreover, the F1-transform makes it possible to estimate the direction of the trend, which can then be characterized by expressions of natural language (stagnating, slightly increasing, sharply decreasing, etc.). Finally, we focus on selected problems of mining information from time series. First, we suggest an algorithm for finding intervals of monotonous behavior and then show how the theory of intermediate quantifiers (a constituent of fuzzy natural logic) and generalized Aristotle's syllogisms can be applied to automatic summarization of information on time series.

Forecasting Direction of Trend of a Group of Analogous Time Series Using F-Transform and Fuzzy Natural Logic

AbstractWe present an idea to group time series according to similarity of their local trends and to predict future direction of the trend of all of them on the basis of forecast of only one representative. First, we assign to each time series an adjoint one, which consists of a sequence of the F1-transform components. Then, they are grouped together according to their similarity, a principal time series is selected in each group and its future course is forecasted. Finally, directions of trends of the other time series from the same group are computed using special methods of fuzzy natural logic.