2020/06/24 by Eduardo Mizraji · 1 citation
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic
paper · doi:10.1093/jigpal/jzaa026
openalex publication_date 2020/06/24 · openalex created_date 2020/08/03 · openalex updated_date 2026/07/28
Abstract In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT.