The Groupoid-Based Logic for Lattice Effect Algebras
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Proceedings |
| Conference | 2017 IEEE 47TH INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC (ISMVL 2017) |
| MU Faculty or unit | |
| 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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