Achieving tightness in dl-programs

Reviewed by Francisco MartinsIn the field of the combination between description logics and rule-based reasoning systems, dl- programs have proved to be a very successful mechanism. One of their recognized shortcomings, however, is their lack of full tightness: the language constructs that feed data from the logic program have a local effect, leaving the knowledge base essentially unchanged throughout. In this paper, we present a construction that we call lifting, which allows predicates to be fully shared between the two components of a dl-program in a systematic way, and show how lifting can be used to provide intuitive solutions to a number of everyday reasoning problems involving the verification of integrity constraints and the implementation of default rules. This construction preserves consistency of the underlying knowledge base and complexity of the overall system. Furthermore, the resulting semantics of default rules has a natural interpretation under the original Reiter semantics

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic