Aristotle’s Syllogisms in Logical Semantics Relying on Optimistic, Average and Pessimistic Membership Functions

Mihálydeák, Tamás

doi:10.1007/978-3-319-08644-6_6

Cited by 3 publications

(3 citation statements)

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“…One possible direction is to analyze the logical laws and inference schemes of the first-order logic in case of different granule systems. The investigation will follow the methods presented in [3,5]. We hope that the result of the planned research could be a calculus over a three-valued partial system relying on the representative-based approximation space.…”

Section: Discussionmentioning

confidence: 99%

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

Kádek¹,

Mihálydeák²

2021

AMI

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The representative-based approximation has been widely studied in rough set theory. Hence, rough set approximations can be defined by the system of representatives, which plays a crucial role in set approximation. In the authors' previous research a possible use of the similarity-based rough set in first-order logic was investigated. Now our focus has changed to representative-based approximation systems. In this article the authors show a logical system relying on representative-based set approximation. In our approach a three-valued partial logic system is introduced. Based on the properties of the approximation space, our theorems prove that in some cases, there exists an efficient way to evaluate the first-order formulae.

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Section: Discussionmentioning

confidence: 99%

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

Kádek¹,

Mihálydeák²

2021

AMI

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“…In this paper there is no enough space to give all proved theorems. In [6,3,4,5] the most important properties are investigated.…”

Section: Central Semantic Notionsmentioning

confidence: 99%

“…For example in [4], Aristotle's syllogisms of the first figure are investigated. These consequence relations represent the most typical usages of quantified propositions containing one-argument predicates.…”

Section: Central Semantic Notionsmentioning

confidence: 99%

Logical Treatment of Incomplete/Uncertain Information Relying on Different Systems of Rough Sets

Mihálydeák¹

2021

Intelligence Science III

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The different systems of rough set theory treat uncertainty in special ways. There is a very important common property: all systems rely on given background knowledge and we cannot say more about an arbitrary set or about its members than its lower and upper approximations make possible. New membership relations have to be introduced. The semantics of classical logic is based on classical set theory. An important question: Is it possible to build logical systems with semantics relying on different versions of the theory of rough sets by using new membership relations? The paper gives an overview of first-order logical systems with partial semantics in order to show the influence of incomplete/uncertain information in logically valid inferences.

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Logic on Similarity Based Rough Sets

Mihálydeák

2018

Rough Sets

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Aristotle’s Syllogisms in Logical Semantics Relying on Optimistic, Average and Pessimistic Membership Functions

Cited by 3 publications

References 10 publications

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

Logical Treatment of Incomplete/Uncertain Information Relying on Different Systems of Rough Sets

Logic on Similarity Based Rough Sets

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