Holistic and Compositional Logics Based on the Bertini Gate

The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic where the meaning of a formula is identified with a density operator and the logical connectives are interpreted as operations defined in terms of quantum gates. We show some relations betwe...

Full description

Saved in:
Bibliographic Details
Published in:Foundations of science 2022-03, Vol.27 (1), p.57-75
Main Author: Leporini, Roberto
Format: Article
Language:English
Subjects:
Algebra
Computer applications
Education
Integrated circuits
Logic
Logic circuits
Mathematical Logic and Foundations
Methodology of the Social Sciences
Operators (mathematics)
Philosophy
Philosophy of Science
Quantum computing
Qubits (quantum computing)
Semantics
Semiconductor chips
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic where the meaning of a formula is identified with a density operator and the logical connectives are interpreted as operations defined in terms of quantum gates. We show some relations between the Bertini gate and many valued connectives by probability values. On this basis, one can deal with quantum circuits as expressions in an algebraic environment such as product many valued algebra for combinational circuits. As can be expected, we show that the compositional logic characterized by the qubit semantics is stronger than the compositional Łukasiewicz quantum computational logic by a counterexample. But, in the holistic case, we conjecture that they can characterize the same logic.
ISSN:1233-1821
1572-8471
DOI:10.1007/s10699-020-09703-y