Fuzzy operator logic and fuzzy resolution

Weigert, Thomas; Tsai, Jeffrey J. P.; Liu, Xuhua

doi:10.1007/bf00881864

Cited by 27 publications

(9 citation statements)

References 21 publications

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“…As said before, our systems are similar to the fuzzy operator logics of Weigert et al [112,158] who presented the theory and resolution procedure of the logics. Fuzzy operator logic also allows the fuzzy operator of a formula, in which the fuzzy operator is regarded as a kind of negation, and we can point out some similarities of FPτ and fuzzy operator logics.…”

Section: Theorem 52 Any Formulas a In Fpτ Can Be Translated As T(a) mentioning

confidence: 86%

“…One of the pioneering works is Lee's [108] paper on the resolution principle for fuzzy logic. We believe that Liu et al's work [112,158] Note that FPτ has no negations, since an annotation acts as a generalized negation. Here, the annotation is a real number.…”

Section: Fuzzy Annotated Logicsmentioning

confidence: 90%

“…FPτ enhances the expressive power of Pτ . In addition, FPτ is closely related to the fuzzy operator logic of Liu et al [112,158].…”

Section: Fuzzy Annotated Logicsmentioning

confidence: 99%

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Introduction to Annotated Logics

Abe¹,

Akama²,

Nakamatsu³

2015

Intelligent Systems Reference Library

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About this SeriesThe aim of this series is to publish a Reference Library, including novel advances and developments in all aspects of Intelligent Systems in an easily accessible and well structured form. The series includes reference works, handbooks, compendia, textbooks, well-structured monographs, dictionaries, and encyclopedias. It contains well integrated knowledge and current information in the field of Intelligent Systems. The series covers the theory, applications, and design methods of Intelligent Systems. Virtually all disciplines such as engineering, computer science, avionics, business, e-commerce, environment, healthcare, physics and life science are included.More information about this series at

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Section: Theorem 52 Any Formulas a In Fpτ Can Be Translated As T(a) mentioning

confidence: 86%

Section: Fuzzy Annotated Logicsmentioning

confidence: 90%

See 1 more Smart Citation

Introduction to Annotated Logics

Abe¹,

Akama²,

Nakamatsu³

2015

Intelligent Systems Reference Library

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“…In Ref. 20, a λ-resolution method is proposed and its completeness proven in the context of operator fuzzy logic. Virtanen in Ref.…”

Section: Related Workmentioning

confidence: 99%

A similarity-based resolution rule

Fontana

Formato

2002

Int. J. Intell. Syst.

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We propose an extension of the resolution rule as the core of a logic programming language based on similarity. Starting from a fuzzy unification algorithm described in Ref. 2 and then extended in Ref. 10, we introduce a fuzzy resolution rule, based on an extended most general unifier supplied by the extended unification algorithm. In our approach, unification fades into a unification degree because of a similarity introduced in a first-order language. Intuitively, the unification degree of a set of first-order terms is the cost one has to pay to consider these terms as equal. For this reason, our extension of the resolution is more structured than its classic counterpart; that is, when the empty clause is reached, in addition to a computed answer, a set of conditions is also determined. We give both the operational and fixed-point semantics of our extended logic programming language, and we prove their equivalence.

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“…In fuzzy logic, each clause has a membership function in [0,1]. Since then subtantial works [5,17,1,13,6,14] have been done on the fuzzy resolution.…”

Section: Introductionmentioning

confidence: 99%

Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra

Nguyen

Doan

et al. 2014

Advances in Intelligent Systems and Computing

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Abstract. The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.

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Fuzzy operator logic and fuzzy resolution

Cited by 27 publications

References 21 publications

Introduction to Annotated Logics

Introduction to Annotated Logics

A similarity-based resolution rule

Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra

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