Bilattice logic properly displayed

Giuseppe Greco; Fei Liang; Alessandra Palmigiano; Umberto Rivieccio

doi:10.1016/j.fss.2018.05.007

Bilattice logic properly displayed

Giuseppe Greco, Fei Liang^*, Alessandra Palmigiano, Umberto Rivieccio

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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	https://doi.org/10.1016/j.fss.2018.05.007
Publication status	Published - 15 May 2019
Externally published	Yes

Keywords

Algebraic proof theory
Bilattice logic
Cut elimination
Display calculi
Many-valued logics
Multi-type calculi
Non-classical logics
Sequent calculi
Substructural logics

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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.",

keywords = "Algebraic proof theory, Bilattice logic, Cut elimination, Display calculi, Many-valued logics, Multi-type calculi, Non-classical logics, Sequent calculi, Substructural logics",

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AU - Greco, Giuseppe

AU - Liang, Fei

AU - Palmigiano, Alessandra

AU - Rivieccio, Umberto

PY - 2019/5/15

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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

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