Some locally tabular logics with contraction and mingle

• Autorzy: Hsieh A.
• Języki publikacji: EN

Abstrakty

EN

Anderson and Belnap�fs implicational system RMO rightwards arrow can be extended conservatively by the usual axioms for fusion and for the Ackermann truth constant t. The resulting system RMO* is algebraized by the quasivariety IP of all idem- potent commutative residuated po-monoids. Thus, the axiomatic extensions of RMO* are in one-to-one correspondence with the relative subvarieties of IP. An algebra in IP is called semiconic if it decomposes subdirectly (in IP) into algebras where the iden- tity element t is order-comparable with all other elements. The semiconic algebras in IP are locally finite. It is proved here that a relative subvariety of IP consists of semiconic algebras if and only if it satisfies x almost equal to (x rightwards arrow t) rightwards arrow x. It follows that if an axiomatic extension of RMO has ((p rightwards arrow t) rightwards arrow p) rightwards arrow p among its theorems then it is locally tabular. In particular, such an extension is strongly decidable, provided that it is finitely axiomatized.

Słowa kluczowe

EN

Residuation; mingle; semiconic; locally tabular; quasivariety

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2010
• Tom: Vol. 45
• Strony: 143--159
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Hsieh A.

• School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa,

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