 These and other problems have led to the exploration and development of other approaches to scientific reasoning, and reasoning in general. Some stick to the probabilistic framework but develop different methodologies within it (Fisher 1925; Neyman and Pearson 1928a,b; Royall 1997; Mayo 1996; Mayo and Spanos 2011; see entry on the  philosophy of statistics).  Others depart from standard probability theory, like  Dempster-Shafer theory  (Shafer 1976; see entry on  formal representations of belief),  a variant of probability theory meant to solve the problem of the priors and make other improvements.  Ranking theory  (Spohn 1988, 2012; again see entry on  formal representations of belief)  also bears some resemblance to probability theory but draws much inspiration from  possible-world semantics for conditionals  (see entry on  indicative conditionals).  Bootstrapping theory (Glymour 1980; Douven and Meijs 2006) leaves the probabilistic framework behind entirely, drawing inspiration instead from the deduction-based approach we began with. Still other approaches develop  non-monotonic logics (see entry),  logics for making not only deductive inferences, but also defeasible, inductive inferences (Pollock 1995, 2008; Horty 2012).  Formal learning theory  provides a framework for studying the long-run consequences of a wide range of methodologies.