What does a conditional knowledge base entail?

Abstract

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...", represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper, S. Kraus and the authors defined and studied "preferential" consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures. This paper studies a more restricted class of consequence relations, "rational" relations. It is argued that any reasonable nonmonotonic inference procedure should define a rational relation. It is shown that the rational relations are exactly those that may be represented by a "ranked" preferential model, or by a (non-standard) probabilistic model. The rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title. Global properties of this closure operation are proved: it is a cumulative operation. It is also computationally tractable. This paper assumes the underlying language is propositional.

Preliminary version presented at KR'89. Minor corrections of the Journal Version

Cited by in corpus (8)

• Reiter's Default Logic Is a Logic of Autoepistemic Reasoning And a Good One, Too
• Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
• Theoretical Foundations of Defeasible Description Logics
• Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
• An Ordinal View of Independence with Application to Plausible Reasoning
• Modal Logics for Qualitative Possibility and Beliefs
• Another perspective on Default Reasoning
• Nonmonotonic inference operations