I am trying to model domain in logic (first order logic or some of modal logics) and I have variable which is degree and not true-false variable. There can be different conclusions depending on the degree of this variable. How to model such variable? If v ir degree variable and n degrees are possible, then v can be modelled by introduction of n propositional variables v1=true <= v=1, v2=true <= v=2 and so on. Additional constraints (axioms) should be introducted - e.g. only one variable from v1, ..., vn can be true.Introduction of additional variables is not good, because: 1) it increases complexity; 2) it is not extendable in simple manner.The question is - maybe there is some syntactic sugar available for degrees, or maybe special logics are already available for handing degrees of even variables whose domain is set of natural numbers?Prolog and other logical programming environments has this feature, maybe this can be brought back to the theory as well.
How to model degree variable in logic (new type of modal logic?)?
lo.logic;logic programming;modal logic