Bøger i Studies in Logic serien

Argumentation is the interdisciplinary study of how conclusions can be reached through the construction and evaluation of arguments, that is, structures describing a proposition together with the reasons for accepting it. The field has received growing interest within Artificial Intelligence over the last decades. It covers aspects of knowledge representation and multi-agent systems, but also touches on various philosophical questions.Phan Minh Dung's abstract argumentation frameworks (AFs) play a dominant role in the field. In AFs arguments and attacks among them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. This book is mainly concerned with the investigation of metalogical properties of Dung's abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics.

Is it possible to conceive two perfectly identical objects? Is identity even possible withoutindividuality? How would a perfectly symmetrical universe be? The current philosophical debate on identity, and in particular on the necessity of the Leibniz's principle of the identity of indiscernibles, is complex and multi-faceted. Recent works have indicated that the problem becomes increasingly complex if we apply it to mathematical objects. Is it possible to speak of 'identity' for numbers? How can we identify numbers?Drawing on philosophical accounts on identity and individuality in contemporary metaphysics (analytic and continental), this book explores a new path. The author argues that an identity without individuality is possible. By means of a critique of the idea of the identity of indiscernibles, the book formulates the concept of 'manifold identity', through the concept of 'iteration'. Iteration is a specific transgression of the identity of indiscernibles arising from the collision of two forms of identity: qualitative identity and numerical identity. Nonetheless, a pair of perfectly identical objects is still a paradox, a contradiction.The first thesis of the book is that iteration is a paraconsistent and dialethetical logical structure, which allows for true contradiction. The author applies recent works in non-standard logic and dialetheism (Priest, Routley, Berto) to illustrate how we can make sense of the idea that objects can be perfectly identical but discernible.The second thesis of the book is that iteration is the basis of enumerability and computability. A 'computable object' is an object constructed on the basis of an iterative logic. It is possible to re-interpret all the primary concepts of computability theory through the logic of iteration.