The Master Argument, recorded by Epictetus, indicates that Diodorus had deduced a contradiction from the conjoint assertion of three propositions. The Argument, which has to do with necessity and contingency and therefore with freedom, has attracted the attention of logicians above all. There have been many attempts at reconstructing it in logical terms, without excessive worry about historical plausibility and with the foregone conclusion that it was sophistic since it directly imperilled our common sense notion of freedom. This text takes exception to recent tradition, translating the propositions into logical terms. The propositions figuring in The Master Argument are interpreted in terms of temporal modal logic where both the modalities and the statements they govern have chronological indices. This means that the force of the argument comes not from purely logical or modal considerations, but from our experience of time.

Nonmonotonic reasoning is a subfield of Artificial Intelligence trying to find more realistic formal models of reasoning than classical logic. In common sense reasoning one often draws conclusions that have to be withdrawn when further information is obtained. The set of conclusions thus does not grow monotonically with the given information. It is this phenomenon that nonmonotonic reasoning methods try to formalize. This volume gives an overview on recent results in the field and points to relevant literature for further study. This up-to-date survey of research in the area of nonmonotonic reasoning includes a concise description of the most influential nonmonotonic logics (e.g. circumscription, autoepistemic logic and default logic), a presentation of recent research in abduction, as well as an overview of semantics for logic programs with default negation. The primary goal of this volume is to make recent results in the field more accessible. An extensive bibliography is included.

Non-well-founded structures arise in a variety of ways in the semantics of both natural and formal languages. Two examples are non-well-founded situations and non-terminating computational processes. A natural modelling of such structures in set theory requires the use of non-well-founded sets. This text presents the mathematical background to the anti-foundation axiom and related axioms that imply the existence of non-well-founded sets when used in place of the axiom of foundation in axiomatic set theory.