Binary resolution over complete residuated Stone lattices

Guller, Dušan

doi:10.1016/j.fss.2007.10.001

Cited by 11 publications

(2 citation statements)

References 5 publications

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“…Reasoning [2,15,16,17,18,45,46,47,50,51,52] can be instrumental in real-world applications that involve uncertainty including inaccuracies and incomplete /ambiguous information. One of the main research directions of intelligent machine information processing regards processing of disparate types of information.…”

Section: Introductionmentioning

confidence: 99%

Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach

Liu¹,

Kaburlasos²,

Hatzimichailidis³

et al. 2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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Automated reasoning can be instrumental in real-world applications involving "intelligent" machines such as (semi-)autonomous vehicles as well as robots. From an analytical point of view, reasoning consists of a series of inferences or, equivalently, implications. In turn, an implication is a function which obtains values in a welldefined set. For instance, in classical Boolean logic an implication obtains values in the set {0, 1}, i.e. it is either true (1) or false (0); whereas, in narrow fuzzy logic an implication obtains values in the specific complete mathematical lattice unit-interval, symbolically [0, 1], i.e. it is partially true/false. A lattice implication algebra (LIA)

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Section: Introductionmentioning

confidence: 99%

Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach

Liu¹,

Kaburlasos²,

Hatzimichailidis³

et al. 2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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show abstract

“…Up to now, many researchers have made some investigation on resolution-based automated reasoning in the framework of many-valued logic, and obtained some important results. 1,8 Xu et al developed α-resolution principle and deduction in latticevalued logic based on lattice implication algebra, 11 and claimed its soundness and completeness. 12,13 Compared with resolution principle in Boolean logic, the α-resolution principle in lattice-valued logic based on lattice implication algebra has some new features.…”

Section: Introductionmentioning

confidence: 99%

NON-CLAUSAL MULTI-ARY α-GENERALIZED RESOLUTION PRINCIPLE FOR A LATTICE-VALUED PROPOSITIONAL LOGIC

Li²,

et al. 2014

Decision Making and Soft Computing

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As a continuation and extension of the established work on binary resolution at certain truth-value level (called α-resolution), this paper introduces nonclausal multi-ary α-generalized resolution principle and deduction for latticevalued propositional logic LP(X) based on lattice implication algebra, which is essentially a non-clausal generalized resolution avoiding the reduction to normal clausal form. Non-clausal multi-ary α-generalized resolution deduction in LP(X) is then proved to be sound and complete.

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On the Satisfiability and Validity Problems in the Propositional Gödel Logic

Guller

2012

Studies in Computational Intelligence

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Binary resolution over complete residuated Stone lattices

Cited by 11 publications

References 5 publications

Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach

Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach

NON-CLAUSAL MULTI-ARY α-GENERALIZED RESOLUTION PRINCIPLE FOR A LATTICE-VALUED PROPOSITIONAL LOGIC

On the Satisfiability and Validity Problems in the Propositional Gödel Logic

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