2 research outputs found
A substructural logic for quantum measurements
This paper presents a substructural logic of sequents with very restricted
exchange and weakening rules. It is sound with respect to sequences of
measurements of a quantic system. A sound and complete semantics is provided.
The semantic structures include a binary relation that expresses orthogonality
between elements and enables the definition of an operation that generalizes
the projection operation in Hilbert spaces. The language has a unitary
connective, a sort of negation, and two dual binary connectives that are
neither commutative nor associative, sorts of conjunction and disjunction. This
provides a logic for quantum measurements whose proof theory is aesthetically
pleasing.Comment: 38 pages, draft to be submitted, comments and remarks welcomed to
[email protected]. This is a corrected, lean, streamlined version of the
previous versio