The Conditional in Mental Probability Logic

Since Störring’s [63] pioneering experiments on syllogistic reasoning at the beginning of last century, experimental psychology has investigated deductive reasoning in the framework of classical logic. The most prominent examples are the theories of mental models [27] and mental rules [8, 59]. A fragment of the model theory of classical logic is central to mental models. Likewise, a fragment of the proof theory of classical logic is central to mental rules. In this tradition, classical logic is considered as the “surest guide” towards a competence model for the psychology of reasoning [38]. Not only did classical logic guide the psychological theories, but it also determined the experimental methodology, and the evaluation of human performance. In the last decade the situation has changed. At present, approaches that extend, or go beyond, classical logic introduce new frameworks in the field. Examples are nonmonotonic reasoning, possibility theory [3], logic programming [61, 62], probabilistic approaches [41, 11, 43, 42, 37, 36, 19, 46, 47, 44] ... [links to other chapters in the book]. The present chapter describes a probabilistic framework of human reasoning. It is based on probability logic. While there are several approaches to probability logic, we adopt the coherence based approach [13, 23]. We assume that rules similar to the principles of probability logic are basic rules of the human inference engine. We therefore call our approach “mental probability logic” [51]. Conditionals are of special importance in the approach. Their interpretation is different from the interpretation in other approaches. We conceive conditionals as non-truth functional, as uncertain, and as nonmonotonic. They allow for exceptions. Below, we call such conditionals “nonmonotonic conditionals”. We note that causal, counterfactual, deontic, or pragmatic conditionals [5] are not in the scope of this chapter, because their logical forms require formalisms that go beyond the scope of the present framework. Causal conditionals require logical operators for intervention, counterfactuals and deontic conditionals require possible worlds