Walter Carnielli – författare

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete.

The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning.

This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency

This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.