A System of Relational Syllogistic Incorporating Full Boolean Reasoning

Ivanov, Nikolay A.; Vakarelov, Dimiter

doi:10.1007/s10849-012-9165-1

Cited by 10 publications

(9 citation statements)

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“…The approach taken by Łukasiewicz and Słupecki is rather idiosyncratic-a more modern style of completeness proof for the same system is given by Shepherdson (1956). A version of the relational syllogistic similarly embedded in propositional logic is investigated by Nishihara et al (1990); see also Ivanov & Vakarelov (2012). Curiously, Leibniz attempted to give a numerical semantics for the Classical syllogistic-a project which does turn out to be realizable (see Sotirov 2012); no interesting computational consequences result, however.…”

Section: )mentioning

confidence: 99%

Semantic Complexity in Natural Language

Pratt-Hartmann

2015

The Handbook of Contemporary Semantic Theory

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Section: )mentioning

confidence: 99%

Semantic Complexity in Natural Language

Pratt-Hartmann

2015

The Handbook of Contemporary Semantic Theory

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“…Syllogistic reasoning is important due to the role they have played in theory and practice of reasoning from Aristotle onwards. Syllogistic reasoning is the most intensively researched in the study of logical reasoning, such as [1][2][3][4][5][6][7][8][9][10]. It is agreed that the appropriate theory of inference should be provided by formal logic, that is, by the theory of what inferences people should draw ( [11], p. 192).…”

Section: Introductionmentioning

confidence: 99%

Screening out All Valid Aristotelian Modal Syllogisms

Zhang¹

2019

ACM

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It is easy to understand that whether a classical syllogism is valid. That whether a modal syllogism is valid is not so transparent. The prevailing view on Aristotelian modal syllogistic is that the syllogistic is incomprehensible due to its many faults and inconsistencies. Although adequate semantic analysis or reconstruction of the syllogistic have be given by many authors, it is far from obvious how to extend these results so as to consistently cover the whole modal syllogistic developed. The major aim of this paper is to overcome these difficulties, and screen out 384 Aristotelian valid modal syllogisms from 6656 Aristotelian modal syllogisms in natural language. They can be formalized by means of set theory and generalized quantifier theory, and their validity can be proved by possible world semantics and the truth definition of Aristotelian quantifiers defined in generalized quantifier theory. The basic steps of screening out all valid Aristotelian modal syllogisms are as follows: firstly one can get all possible modal syllogisms obtained by adding modal operators to 24 valid classical syllogisms, and secondly eliminate invalid modal syllogisms by characteristic rules of modal syllogisms. It is hoped that these innovative achievements will make contributions to promote the development of Aristotelian and generalized modal syllogistic, natural language information processing, and further research on knowledge representation and knowledge reasoning in computer science.

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“…Syllogistic logic has already been studied from the perspective of generalized quantifier theory [9][10][11][12]. Although there are many other articles about Aristotelian syllogisms [13]- [18], we are not aware of axiomatization of Aristotelian syllogisms by means of generalized quantifier theory, and so this is a goal of the paper.…”

Section: Introductionmentioning

confidence: 99%

Axiomatization of Aristotelian Syllogistic Logic Based on Generalized Quantifier Theory

Zhang¹

2018

ACM

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Syllogistic reasoning is important due to the prominence of syllogistic arguments in human reasoning, and also to the role they have played in theory of reasoning from Aristotle onwards. Aristotelian syllogistic logic is a formal study of the meaning of four Aristotelian quantifiers and of their properties. This paper focuses on logical system based on syllogistic reasoning. It firstly formalized the 24 valid Aristotle's syllogisms, and then has proven that the other 22 valid Aristotle's syllogisms can be derived from the syllogisms 'Barbara' AAA-1 and 'Celarent' EAE-1 by means of generalized quantifier theory and set theory, so the paper has completed the axiomatization of Aristotelian syllogistic Logic. This axiomatization needs to make full use of symmetry and transformable relations between/among the monotonicity of the four Aristotelian quantifiers from the perspective of generalized quantifier theory. In fact, these innovative achievements and the method in this paper provide a simple and reasonable mathematical model for studying other generalized syllogisms. It is hoped that the present study will make contributions to the development of generalized quantifier theory, and to bringing about consequences to natural language information processing as well as knowledge representation and reasoning in computer science.

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A System of Relational Syllogistic Incorporating Full Boolean Reasoning

Cited by 10 publications

References 26 publications

Semantic Complexity in Natural Language

Semantic Complexity in Natural Language

Screening out All Valid Aristotelian Modal Syllogisms

Axiomatization of Aristotelian Syllogistic Logic Based on Generalized Quantifier Theory

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