Vector logic and counterfactuals
share
In this work we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vectors formalism for logical functions and truth values. With this formalism, we can describe the counterfactuals as complex matrix operators that appear preprocessing the implication matrix with one of the square roots of the negation, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. The reason of this fact, is that this representation of a counterfactual proposition produces a valuation that is the superposition the two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure produces a uncertain evaluation projected on the complex domain. After this basic representation, the judgment of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal represented by the real vectors 'true' or 'false', and we can represent symbolically this shift applying for a second time the two square roots of the negation.
READ FULL TEXT