An Unsharp Logic from Quantum Computation

AbstractLogical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the $$\sqrt {NOT} $$ (which admit of natural physical models). This leads to a semantic characterization of a logic that we call quantum computational logic (QCL).