Computer Engineering / Bilgisayar Mühendisliği

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End date: 2019Subject: search.filters.subject.Syllogistic reasoning

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Now showing 1 - 8 of 8
  • Conference Object
    Citation - WoS: 3
    Citation - Scopus: 6
    Truth Ratios of Syllogistic Moods
    (Institute of Electrical and Electronics Engineers, 2015) Zarechnev, Mikhail; Kumova, Bora İsmail
    The syllogistic system consists of 256 moods, of which only 24 have been recognized as true. From a set-theoretical point of view, a mood can be represented with three sets and their possible relationships. Three sets can have up to seven sub-sets or spaces. In an earlier work we have used 41 permutations of the spaces, out of which every mood matches an individual number as true or false cases. The truth ratio of a mood is then calculated, by relating the true and false cases with each other. In this work we revise the previously presented properties of the moods and the syllogistic system, this time by using the maximum possible cover, which consists of 96 distinct space permutations. Our results mostly verify our previous findings, like the additional true mood anasoy, the inherently symmetric truth distribution of the moods. Additionally we have revealed some new properties, like the equivalence of some moods, which reduces the system to 136 distinct moods.
  • 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: 2
    Citation - Scopus: 2
    An Extended Syllogistic Logic for Automated Reasoning
    (Institute of Electrical and Electronics Engineers, 2017) Çine, Ersin; Kumova, Bora İsmail
    In this work, we generalise the categorical syllogistic logic in several dimensions to a relatively expressive logic that is sufficiently powerful to encompass a wider range of linguistic semantics. The generalisation is necessary in order to eliminate the existential ambiguity of the quantifiers and to increase expressiveness, practicality, and adaptivity of the syllogisms. The extended semantics is expressed in an extended syntax such that an algorithmic solution of the extended syllogisms can be processed. Our algorithmic approach for deduction in this logic allows for automated reasoning directly with quantified propositions, without reduction of quantifiers.
  • Conference Object
    Syllogistic Knowledge Bases With Description Logic Reasoners
    (IEEE, 2018) Çine, Ersin
    Reasoning is a core topic both for natural intelligence and for artificial intelligence. While syllogistic logics (SLs) are often studied by cognitive scientists for understanding human reasoning, description logics (DLs) are usually studied by computer scientists for performing automated reasoning. Although the studies on both of these logics are extensive, their literatures are interestingly isolated from each other. Firstly, we formally define a practical family of SLs with different levels of expressivity, including a logic which has recently been introduced for automated reasoning. Then, we reveal their theoretical properties either by defining direct algorithms for deductive reasoning or by translation rules for them into relevant DLs. These algorithms and rules prove that (i) two of our SLs (namely PolSyl and NegSyl) are tractable fragments of DLs, and (ii) other two SLs (namely ComSyl and ComSyl+) are categorical fragments of DL AEC and DL AEC:0 with general TBoxes, respectively. These findings bridge the gap between (ancient) SLs and (modern) DLs. An immediate result is that it is possible to combine powerful features of both logics, for example, intuitional user interface of an SL and efficient reasoning algorithms for a DL. Finally, we propose a framework for knowledge representation in SLs and link it to sound and complete DL reasoners for automated deduction.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    Generating Ontologies From Relational Data With Fuzzy-Syllogistic Reasoning
    (Springer Verlag, 2015) Kumova, Bora İsmail
    Existing standards for crisp description logics facilitate information exchange between systems that reason with crisp ontologies. Applications with probabilistic or possibilistic extensions of ontologies and reasoners promise to capture more information, because they can deal with more uncertainties or vagueness of information. However, since there are no standards for either extension, information exchange between such applications is not generic. Fuzzy-syllogistic reasoning with the fuzzy-syllogistic system4S provides 2048 possible fuzzy inference schema for every possible triple concept relationship of an ontology. Since the inference schema are the result of all possible set-theoretic relationships between three sets with three out of 8 possible fuzzy-quantifiers, the whole set of 2048 possible fuzzy inferences can be used as one generic fuzzy reasoner for quantified ontologies. In that sense, a fuzzy syllogistic reasoner can be employed as a generic reasoner that combines possibilistic inferencing with probabilistic ontologies, thus facilitating knowledge exchange between ontology applications of different domains as well as information fusion over them.
  • 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 - 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.