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. (shrink)

The Jain logic addresses concerns elicited by sense experience of observable and measurable reality. Reality is what it is, and it exists independent of the observer. The last Jain Tirthankar Mahaveer suggested that organisms interact with such realities for survival needs and become concerned about the consequences. He suggested a code of conduct for reality-based behaviors to address concerns. Perceptions and impressions provide measures of information in sense experience, and with other evidence guide choices and decisions to act and bear (...) consequences. Ethical behaviors rooted in reality have desirable consequences, and inconsistent and contradictory behaviors are undesirable consequences. Omniscience is discarded as a self-referential ad hoc construct inconsistent and contradictory to real world behaviors. This article is survey of assumptions and models to represent, interpret, and validate knowledge that begins with logical deduction for inference based on evidence from sense experience. Secular and atheistic thrust of thought and practice encourages reasoning and open-ended search with affirmed assertions and independent evidence. Individual identity emerges with consistent behaviors to overcome fallibility and unreliability by minimizing doubt. The first Tirthankar Rishabh Nath suggested that the content of real and abstract objects and concerns during a change is conserved as the net balance of the inputs and outputs. Identity and content of assertions and evidence is also conserved during logical manipulations for reasoning. Each assertion and its negation are to be affirmed with independent evidence, and lack of evidence for presence is not necessarily the evidence for either non-absence or non-existence. (shrink)