The Groupoid-Based Logic for Lattice Effect Algebras

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Authors

CHAJDA Ivan LÄNGER Helmut PASEKA Jan

Year of publication 2017
Type Article in Proceedings
Conference 2017 IEEE 47TH INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC (ISMVL 2017)
MU Faculty or unit

Faculty of Science

Citation
Web http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7964996
Doi http://dx.doi.org/10.1109/ISMVL.2017.15
Field General mathematics
Keywords D-poset; effect algebra; lattice effect algebra; antitone involution; effect groupoid; groupoid-based logic
Description The aim of the paper is to establish a certain logic corresponding to lattice effect algebras. First, we answer a natural question whether a lattice effect algebra can be represented by means of a groupoid-like structure. We establish a one-to-one correspondence between lattice effect algebras and certain groupoids with an antitone involution. Using these groupoids, we are able to introduce a suitable logic for lattice effect algebras.
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