Commonsense knowledge representation and reasoning with fuzzy neural networks

This paper highlights the theory of common-sense knowledge in terms of representation and reasoning. A connectionist model is proposed for common-sense knowledge representation and reasoning. A generic fuzzy neuron is employed as a basic element for the connectionist model. The representation and reasoning ability of the model is described through examples

Development of fuzzy syllogistic algorithms and applications distributed reasoning approaches

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2010Includes bibliographical references (leaves: 44-45)Text in English; Abstract: Turkish and Englishx, 65 leavesA syllogism, also known as a rule of inference or logical appeals, is a formal logical scheme used to draw a conclusion from a set of premises. It is a form of deductive reasoning that conclusion inferred from the stated premises. The syllogistic system consists of systematically combined premises and conclusions to so called figures and moods. The syllogistic system is a theory for reasoning, developed by Aristotle, who is known as one of the most important contributors of the western thought and logic. Since Aristotle, philosophers and sociologists have successfully modelled human thought and reasoning with syllogistic structures. However, a major lack was that the mathematical properties of the whole syllogistic system could not be fully revealed by now. To be able to calculate any syllogistic property exactly, by using a single algorithm, could indeed facilitate modelling possibly any sort of consistent, inconsistent or approximate human reasoning. In this work generic fuzzifications of sample invalid syllogisms and formal proofs of their validity with set theoretic representations are presented. Furthermore, the study discuss the mapping of sample real-world statements onto those syllogisms and some relevant statistics about the results gained from the algorithm applied onto syllogisms. By using this syllogistic framework, it can be used in various fields that can uses syllogisms as inference mechanisms such as semantic web, object oriented programming and data mining reasoning processes

Fuzzy Natural Logic in IFSA-EUSFLAT 2021

The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications

A Fuzzy Syllogistic Reasoning Schema for Generalized Quantifiers

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimization problem, where the premises constitute the constraints of the searching space for the quantifier in the conclusion.Comment: 22 pages, 6 figures, journal pape

How to Obtain Valid Generalized Modal Syllogisms from Valid Generalized Syllogisms

Making full use of the truth value definitions of sentences with quantification, possible world semantics and/or fuzzy logic, one can prove the validity of generalized modal syllogisms. This paper shows that the proof of the validity of a generalized modal syllogism can be transformed into that of its corresponding generalized syllogism, and that the generalized syllogism obtained by removing all modalities in any valid generalized modal syllogism is still valid. Therefore, the simplest way to screen out valid generalized modal syllogisms is to add modalities to valid generalized syllogisms, and then to delete all invalid syllogisms by means of the basic rules with which valid generalized modal syllogisms should meet. And then the remainders are valid. This paper illustrates how to obtain 12 valid generalized modal syllogisms by adding necessary modalities and/or possible modalities to any valid generalized syllogism. The two kinds of syllogisms discussed in this paper are composed of sentences with quantification which is the largest number of sentences in natural language. Hence, this innovative research can provide theoretical support for linguistics, logic, artificial intelligence, and among other fields

Contextuality: A Philosophical Paradigm, with Applications to Philosophy of Cognitive Science

We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and lessincompleteness. We state that all logics, and also truth judgements, are contextdependent, and we develop a “Context-dependant Logic”. We apply ideas of Contextuality to problems in semantics, the problem of “where is the mind”, and the study of consciousness

Reduction between Categorical Syllogisms Based on the Syllogism EIO-2

Syllogism reasoning is a common and important form of reasoning in human thinking from Aristotle onwards. To overcome the shortcomings of previous studies, this article makes full use of set theory and classical propositional logic, and deduces the remaining 23 valid syllogisms only on the basis of the syllogism EIO-2 from the perspective of mathematical structuralism, and then successfully establishes a concise formal axiom system for categorical syllogistic logic. More specifically, the article takes advantage of the trisection structure of categorical propositions such as Q(a, b), the transformation relations between an Aristotelian quantifier and its inner and outer negation, the symmetry of the two Aristotelian quantifier (that is, no and some), and some inference rules in classical propositional logic, and derives the remaining 23 valid syllogisms from the syllogism EIO-2, so as to realize the reduction between different valid categorical syllogisms