Fuzzy-Syllogistic Systems: A Generic Model for Approximate Reasoning

Kumova, Bora I.

doi:10.1007/978-3-319-42007-3_15

Cited by 2 publications

(1 citation statement)

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“…Currently we are testing the feasibility of the generic system n S on fuzzy-syllogistic ontologies [20] and fuzzy-syllogistic reasoning with such ontologies [21,42]. Everyone of the 25 true moods has a point-symmetric counterpart, in terms of the particular cases they match.…”

Section: Discussionmentioning

confidence: 99%

Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition

Kumova

2017

Studies in Universal Logic

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The logical square has a simple symmetric structure that visualises the bivalent relationships of the classical quantifiers A, I, E, O. In philosophy it is perceived as a self-complete possibilistic logic. In linguistics however its modelling capability is insufficient, since intermediate quantifiers like few, half, most, etc cannot be distinguished, which makes the existential quantifier I too generic and the universal quantifier A too specific. Furthermore, the latter is a special case of the former, i.e. A I, making the square a logic with inclusive quantifiers. The inclusive quantifiers I and O can produce redundancies in linguistic systems and are too generic to differentiate any intermediate quantifiers. The redundancy can be resolved by excluding A from I, i.e. 2 IDI-A, analogously E from O, i.e. 2 ODO-E. Although the philosophical possibility of A I is thus lost in 2 I, the symmetric structure of the exclusive square 2 remains preserved. The impact of the exclusion on the traditional syllogistic system S with inclusive existential quantifiers is that most of its symmetric structures are obviously lost in the syllogistic system 2 S with exclusive existential quantifiers too. Symmetry properties of S are found in the distribution of the syllogistic cases that are matched by the moods and their intersections. A syllogistic case is a distinct combination of the seven possible spaces of the Venn diagram for three sets, of which there exist 96 possible cases. Every quantifier can be represented with a fixed set of syllogistic cases and so the moods too. Therefore, the 96 cases open a universe of validity for all moods of the syllogistic system S, as well as all fuzzy-syllogistic systems n S, with n-1 intermediate quantifiers. As a by-product of the fuzzy syllogistic system and its properties, we suggest in return that the logical square of opposition can be generalised to a fuzzy-logical graph of opposition, for 2

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Section: Discussionmentioning

confidence: 99%

Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition

Kumova

2017

Studies in Universal Logic

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An extended syllogistic logic for automated reasoning

Cine

Kumova

2017

2017 International Conference on Computer Science and Engineering (UBMK)

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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.-Automated deduction, automated reasoning, knowledge representation, syllogistic reasoning.

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Fuzzy-Syllogistic Systems: A Generic Model for Approximate Reasoning

Cited by 2 publications

References 24 publications

Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition

Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition

An extended syllogistic logic for automated reasoning

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