Original title:
On the Failure of Strong Standard Completness in PiMTL
Translated title:
O neplatnosti věty o silné standardní úplnosti logiky PiMTL
Authors:
Horčík, Rostislav Document type: Papers Conference/Event: The Logic of Soft Computing /4./, Workshop of the ERCIM Working Group on Soft Computing, Ostrava (CZ), 2005-10-05 / 2005-10-07
Year:
2005
Language:
eng Abstract:
[eng][cze] It is well-known that Hájek s basic fuzzy logic (BL), Lukasiewicz logic, and product logic are not strongly standard complete. On the other hand Esteva and Godo s monoidal t-norm logic (MTL) and its involutive extension IMTL are strongly standard complete. In this paper we show that PiMTL (an extension of MTL by the axioms characteristic of product logic) does not enjoy the strong standard completeness theorem like BL, Lukasiewicz, and product logic.Je dobře známo, že logiky: basic fuzzy logic (BL), Lukasiewicz logic a product logic, nesplňují větu o silné standardní úplnosti. Na druhou stranu monoidal t-norm logic (MTL) a její involutivní axiomatické rozšíření IMTL tuto větu splňují. V tomto článku ukážeme, že logika PiMTL (t.j. axiomatické rozšíření MTL o axiomy charakteristické pro product logic) nesplňuje větu o silné standardní úplnosti podobně jako logiky: BL, Lukasiewicz logic, product logic.
Keywords:
monoidal t-norm logic; MTL-algebra; strong standard completeness Project no.: CEZ:AV0Z10300504 (CEP), IAA100300503 (CEP) Funding provider: GA AV ČR Host item entry: Proceedings
Institution: Institute of Computer Science AS ČR
(web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences. Original record: http://hdl.handle.net/11104/0125722