Conditionals and Modularity in General Logics

This book covers modularity and independence in classical and nonclassical logic, including many-valued logics and structures, plus neighbourhood semantics and their connection to independence, as well as their common points and differences for various logics.

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation.

The book will be of value to researchers and graduate students in logic and theoretical computer science.

The authors present results on modularity and interpolation for monotonic and nonmonotonic logic, using a semantic approach and revealing new insights. The first monograph on this topic. This book is useful for researchers and advanced students.

Auteur
The first author is one of the foremost authorities on nonclassical logics and their applications in computing, the second author has written three related research monographs.

Contenu

Introduction; Basic Definitions; Towards a Uniform Picture of Conditionals; Monotone and Antitone Semantic and Syntactic Interpolation; Laws About Size and Interpolation in Nonmonotonic Logics; Neighbourhood Semantics; Conclusion and Outlook; References; Index