When Conditional Logic and Belief Revision Meet Substructural Logics

Abstract : Two threads of research have been pursued in parallel in logic and artificial intelligence. On the one hand, in artificial intelligence, logic-based theories have been developed to study and formalize belief change and the so-called "common sense reasoning" , i.e. the actual reasoning of humans. On the other hand, in logic, substructural logics, i.e. logics lacking some of the structural rules of classical logic, have been studied in depth from a theoretical point of view. However, the powerful (proof-theoretical) techniques and methods developed in logic have not yet been applied to artificial intelligence. Conditional logic and belief revision theory are prominent theories in artificial intelligence dealing with common sense reasoning. We show in this article that they can both be embedded within the framework of substructural logics and can both be seen as extensions of the Lambek calculus. This allows us to compare and relate them to each other systematically, via a natural formalization of the Ramsey test.
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Guillaume Aucher. When Conditional Logic and Belief Revision Meet Substructural Logics. DARe-15 2015 Defeasible and Ampliative Reasoning, Jul 2015, Buenos Aires, Argentina. ⟨hal-01193289⟩

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