Abstract
We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut elimination. Our proposal builds on the product representation of bilattices and applies the guidelines of the multi-type methodology in the design of display calculi.
| Original language | English |
|---|---|
| Pages (from-to) | 138-155 |
| Number of pages | 18 |
| Journal | Fuzzy Sets and Systems |
| Volume | 363 |
| DOIs | |
| Publication status | Published - 15 May 2019 |
| Externally published | Yes |
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Keywords
- Algebraic proof theory
- Bilattice logic
- Cut elimination
- Display calculi
- Many-valued logics
- Multi-type calculi
- Non-classical logics
- Sequent calculi
- Substructural logics
Cite this
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Bilattice logic properly displayed. / Greco, Giuseppe; Liang, Fei; Palmigiano, Alessandra; Rivieccio, Umberto.
In: Fuzzy Sets and Systems, Vol. 363, 15.05.2019, p. 138-155.Research output: Contribution to Journal › Article › Academic › peer-review
TY - JOUR
T1 - Bilattice logic properly displayed
AU - Greco, Giuseppe
AU - Liang, Fei
AU - Palmigiano, Alessandra
AU - Rivieccio, Umberto
PY - 2019/5/15
Y1 - 2019/5/15
N2 - We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut elimination. Our proposal builds on the product representation of bilattices and applies the guidelines of the multi-type methodology in the design of display calculi.
AB - We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut elimination. Our proposal builds on the product representation of bilattices and applies the guidelines of the multi-type methodology in the design of display calculi.
KW - Algebraic proof theory
KW - Bilattice logic
KW - Cut elimination
KW - Display calculi
KW - Many-valued logics
KW - Multi-type calculi
KW - Non-classical logics
KW - Sequent calculi
KW - Substructural logics
UR - http://www.scopus.com/inward/record.url?scp=85047217089&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85047217089&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2018.05.007
DO - 10.1016/j.fss.2018.05.007
M3 - Article
VL - 363
SP - 138
EP - 155
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
SN - 0165-0114
ER -