HAL CCSD
Quantum Inspired Eigenlogic and Truth Table Semantics
Toffano, Zeno
Laboratoire des signaux et systèmes (L2S) ; Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
CentraleSupélec
Université Paris-Saclay
International audience
Quantum and Physics Logic (QPL) 2020
Paris, France
hal-02859818
https://centralesupelec.hal.science/hal-02859818
https://centralesupelec.hal.science/hal-02859818/document
https://centralesupelec.hal.science/hal-02859818/file/QPL_2020_paper_18%282%29.pdf
https://centralesupelec.hal.science/hal-02859818
Quantum and Physics Logic (QPL) 2020, Jun 2020, Paris, France
en
[MATH.MATH-LO]Mathematics [math]/Logic [math.LO]
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
info:eu-repo/semantics/conferenceObject
Conference papers
Eigenlogic proposes a new method in logic inspired from quantum theory using operators. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet {0,1} using projection operators to the binary alphabet {+1,-1} employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley-Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement.
2020-06-02
info:eu-repo/semantics/OpenAccess