Computer Engineering / Bilgisayar Mühendisliği

Permanent URI for this collectionhttps://hdl.handle.net/11147/10

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Institution Author: search.filters.institutionAuthor.Kumova, Bora İsmailSubject: search.filters.subject.Approximate reasoning

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Now showing 1 - 5 of 5
  • Conference Object
    Citation - Scopus: 1
    Fuzzy-Syllogistic Systems: a Generic Model for Approximate Reasoning
    (Springer, 2016) Kumova, Bora İsmail
    The well known Aristotelian syllogistic system S consists of 256 moods. We have found earlier that 136 moods are distinct in terms of equal truth ratios that range in tau = [ 0,1]. The truth ratio of a particular mood is calculated by relating the number of true and false syllogistic cases that the mood matches. The introduction of (n -1) fuzzy existential quantifiers, extends the system to fuzzy-syllogistic systems S-n, 1 < n, of which every fuzzy-syllogistic mood can be interpreted as a vague inference with a generic truth ratio, which is determined by its syllogistic structure. Here we introduce two new concepts, the relative truth ratio (r)tau = [ 0,1] that is calculated from the cardinalities of the syllogistic cases of the mood and fuzzy-syllogistic ontology (FSO). We experimentally apply the fuzzy-syllogistic systems S-2 and S-6 as underlying logic of a FSO reasoner (FSR) and discuss sample cases for approximate reasoning.y
  • Conference Object
    Citation - WoS: 5
    Citation - Scopus: 8
    The Fuzzy Syllogistic System
    (Springer Verlag, 2010) Kumova, Bora İsmail; Çakır, Hüseyin
    A categorical syllogism is a rule of inference, consisting of two premisses and one conclusion. Every premiss and conclusion consists of dual relationships between the objects M, P, S. Logicians usually use only true syllogisms for deductive reasoning. After predicate logic had superseded syllogisms in the 19th century, interest on the syllogistic system vanished. We have analysed the syllogistic system, which consists of 256 syllogistic moods in total, algorithmically. We have discovered that the symmetric structure of syllogistic figure formation is inherited to the moods and their truth values, making the syllogistic system an inherently symmetric reasoning mechanism, consisting of 25 true, 100 unlikely, 6 uncertain, 100 likely and 25 false moods. In this contribution, we discuss the most significant statistical properties of the syllogistic system and define on top of that the fuzzy syllogistic system. The fuzzy syllogistic system allows for syllogistic approximate reasoning inductively learned M, P, S relationships.
  • Conference Object
    Citation - Scopus: 1
    Approximate Reasoning With Fuzzy-Syllogistic Systems
    (CEUR Workshop Proceedings, 2015) Kumova, Bora İsmail
    The well known Aristotelian syllogistic system consists of 256 moods. We have found earlier that 136 moods are distinct in terms of equal truth ratios that range in τ=[0,1]. The truth ratio of a particular mood is calculated by relating the number of true and false syllogistic cases the mood matches. A mood with truth ratio is a fuzzy-syllogistic mood. The introduction of (n-1) fuzzy existential quantifiers extends the system to fuzzy-syllogistic systems nS, 1<n, of which every fuzzy-syllogistic mood can be interpreted as a vague inference with a generic truth ratio that is determined by its syllogistic structure. We experimentally introduce the logic of a fuzzy-syllogistic ontology reasoner that is based on the fuzzy-syllogistic systems nS. We further introduce a new concept, the relative truth ratio rτ=[0,1] that is calculated based on the cardinalities of the syllogistic cases.
  • Conference Object
    Citation - Scopus: 3
    Ontology-Based Fuzzy-Syllogistic Reasoning
    (Springer Verlag, 2015) Zarechnev, Mikhail; Kumova, Bora İsmail
    We discuss the Fuzzy-Syllogistic System (FSS) that consists of the well-known 256 categorical syllogisms, namely syllogistic moods, and Fuzzy- Syllogistic Reasoning (FSR), which is an implementation of the FSS as one complex approximate reasoning mechanism, in which the 256 moods are interpreted as fuzzy inferences. Here we introduce a sample application of FSR as ontology reasoner. The reasoner can associate up to 256 possible fuzzyinferences with truth ratios in [0,1] for every triple concept relationship of the ontology. We further discuss a transformation technique, by which the truth ratio of a fuzzy-inference can increase, by adapting the fuzzy-quantifiers of a fuzzy-inference to the syllogistic logic of the sample propositions.
  • Conference Object
    Citation - WoS: 5
    Citation - Scopus: 10
    Algorithmic Decision of Syllogisms
    (Springer Verlag, 2010) Kumova, Bora İsmail; Çakır, Hüseyin
    A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. In a categorical syllogisms, every premise and conclusion is given in form a of quantified relationship between two objects. 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 paper we present such an algorithm.