×

Effectiveness and multivalued logics. (English) Zbl 1106.03018

This paper offers an interesting combination of ideas from the fields of domain theory and of fuzzy logic, the latter one understood as an infinite-valued logic with graded notions of validity and provability, i.e., as a logic which allows inferences from fuzzy sets of formulas. He basically considers the lattice \(L^S\) of all \(L\)-fuzzy subsets over a codable universe of discourse \(S\), with \(L\) an effective (based) continuous lattice.
With reference to his abstract setting for fuzzy logic, as introduced in his monograph [Fuzzy logic. Mathematical tools for approximate reasoning. Kluwer Academic Publishers, Dordrecht (2001; Zbl 0976.03026)], the author discusses in the previously mentioned context semi-decidablity properties of fuzzy theories.

MSC:

03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
06B35 Continuous lattices and posets, applications
03D45 Theory of numerations, effectively presented structures
03B25 Decidability of theories and sets of sentences

Citations:

Zbl 0976.03026
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Synthese 19 pp 325– (1968)
[2] DOI: 10.1007/BF00372547 · Zbl 0645.03053 · doi:10.1007/BF00372547
[3] Possibility theory: An approach to computerized processing of uncertainty (1988)
[4] DOI: 10.1002/malq.19860321906 · Zbl 0583.03043 · doi:10.1002/malq.19860321906
[5] DOI: 10.1007/s001530100128 · Zbl 1024.03024 · doi:10.1007/s001530100128
[6] DOI: 10.1002/malq.19890350107 · Zbl 0649.03031 · doi:10.1002/malq.19890350107
[7] Information Sciences 9 pp 301– (1975)
[8] DOI: 10.1016/0304-3975(77)90045-7 · Zbl 0429.03028 · doi:10.1016/0304-3975(77)90045-7
[9] A mathematical theory of evidence (1976) · Zbl 0359.62002
[10] Die Nichaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz 27 pp 159– (1962)
[11] DOI: 10.1002/malq.19790250304 · Zbl 0435.03020 · doi:10.1002/malq.19790250304
[12] Mathematical principles of fuzzy logic (1999) · Zbl 0940.03028
[13] DOI: 10.1023/A:1011958407631 · Zbl 0985.03014 · doi:10.1023/A:1011958407631
[14] Metamathematics of fuzzy logic (1998) · Zbl 0937.03030
[15] A treatise on many-valued logics (2000)
[16] Algebraic foundations of many-valued reasoning (2000) · Zbl 0937.06009
[17] DOI: 10.1006/jmaa.1997.5659 · Zbl 0891.03006 · doi:10.1006/jmaa.1997.5659
[18] DOI: 10.1016/0004-3702(94)90102-3 · Zbl 0821.03014 · doi:10.1016/0004-3702(94)90102-3
[19] Fuzzy logic: Mathematical tools for approximate reasoning (2001) · Zbl 0976.03026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.