Algebraic axiomatization of tense intuitionistic logic

• Autorzy: Ivan Chajda
• Języki publikacji: EN

Abstrakty

EN

We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame.

Słowa kluczowe

EN

Brouwerian lattice; Heyting algebra; Complete lattice; Relative pseudocomplementation; Tense operators; Intuitionistic logic

Kategorie tematyczne

• 03B44: Temporal logic
• 03G25: Other algebras related to logic
• 06D20: Heyting algebras
• 03G10: Lattices and related structures

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 1185-1191

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Ivan Chajda

• Palacký University Olomouc

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0063-6