TY - CHAP
T1 - On Non-deterministic Functional Completeness
AU - Avron, Arnon
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - We introduce N-functional completeness as a natural generalization to non-deterministic matrices of the notion of functional completeness in ordinary (deterministic) matrices. We also provide an effective criterion for N-functional completeness. Then we show that in the two-valued case the set {→,∼} is N-functionally complete, where → is the classical implication, and ∼ is a unary, non-deterministic, semi-negation. We also present a single ternary two-valued non-deterministic connective which is N-functionally complete, and show that no single binary connective can have this property.
AB - We introduce N-functional completeness as a natural generalization to non-deterministic matrices of the notion of functional completeness in ordinary (deterministic) matrices. We also provide an effective criterion for N-functional completeness. Then we show that in the two-valued case the set {→,∼} is N-functionally complete, where → is the classical implication, and ∼ is a unary, non-deterministic, semi-negation. We also present a single ternary two-valued non-deterministic connective which is N-functionally complete, and show that no single binary connective can have this property.
UR - http://www.scopus.com/inward/record.url?scp=85198361633&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-56595-3_3
DO - 10.1007/978-3-031-56595-3_3
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???
AN - SCOPUS:85198361633
T3 - Synthese Library
SP - 83
EP - 92
BT - Synthese Library
PB - Springer Science and Business Media B.V.
ER -