Consider the frequentist argument: "I will believe A since not-A makes the data improbable". Consider the Bayesian argument: "I will believe A since given my beliefs on A and the data generating process, it is more probable than not-A".
Are there any other argument types and how would you construct an argument? (Fiducial? Fuzzy logic? Dempster-Shafer? Possibility theory? Bounds? ...)