# Algebraic axiomatization of tense intuitionistic logic

Open Mathematics (2011)

- Volume: 9, Issue: 5, page 1185-1191
- ISSN: 2391-5455

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topIvan Chajda. "Algebraic axiomatization of tense intuitionistic logic." Open Mathematics 9.5 (2011): 1185-1191. <http://eudml.org/doc/269762>.

@article{IvanChajda2011,

abstract = {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.},

author = {Ivan Chajda},

journal = {Open Mathematics},

keywords = {Brouwerian lattice; Heyting algebra; Complete lattice; Relative pseudocomplementation; Tense operators; Intuitionistic logic; tense intuitionistic logic; algebraic semantics; tense operator; complete lattice; relative pseudocomplementation},

language = {eng},

number = {5},

pages = {1185-1191},

title = {Algebraic axiomatization of tense intuitionistic logic},

url = {http://eudml.org/doc/269762},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Ivan Chajda

TI - Algebraic axiomatization of tense intuitionistic logic

JO - Open Mathematics

PY - 2011

VL - 9

IS - 5

SP - 1185

EP - 1191

AB - 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.

LA - eng

KW - Brouwerian lattice; Heyting algebra; Complete lattice; Relative pseudocomplementation; Tense operators; Intuitionistic logic; tense intuitionistic logic; algebraic semantics; tense operator; complete lattice; relative pseudocomplementation

UR - http://eudml.org/doc/269762

ER -

## References

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