In this paper we investigate nonmonotonic'modes of inference'. Our approach uses modal (conditional) logic to establish a uniform framework in which to study nonmonotonic consequence. We consider a particular mode of inference which employs a majority-based account of default reasoning--one which differs from the more familiar preferential accounts--and show how modal logic supplies a framework which facilitates analysis of, and comparison with more traditional formulations of nonmonotonic consequence.
Recently, conditional logics have been developed for application to problems in default reasoning. We present a uniform framework for the development and investigation of conditional logics to represent and reason with "normality", and demonstrate these logics to be equivalent to extensions of the modal system S4. We also show that two conditional logics, recently proposed to reason with default knowledge, are equivalent to fragments of two logics developed in this framework.
Philippe Lamarre* Robotics Laboratory Department of Computer Science Stanford University Stanford, Ca. 94305 Abstract A large number of common sense assertions such as prototypical properties, obligation, possibility, nonmonotonic rules, can be expressed using conditional logics. They are precisely under the lights because of their great representation power for common sense notions. But representation is only the half of the work: reasoning is also needed. For this last point it is well known that the deduction relations of conditional logics are powerless . In this article we propose to use conditional logics to represent defensible rules and we present different ways, based on semantics, to increase their deductive power. This leads to different nonmonotonic systems, the less powerful being equivalent to Pearl's system Z. A tableau like theorem proving method is proposed to implement all of these formalisms. 1 Introduction. The family of formal systems named conditional logics has been introduced at the end of the sixties with the aim of giving a formal account of linguistic structures of the form if it where the case that...then it would be the case that... ([Lew73], [Sta68], [NutS0], ...). More recently, these systems have been used to deal with a main problem of artificial intelligence: nonmonotonic reasoning.
Conditional Zogics play an important role in recent attempts to investigate default reasoning. This paper investigates firstorder conditional logic. We show that, as for first-order probabilistic logic, it is important not to confound statistical conditionals over the domain (such as "most birds fly"), and subjective conditionals over possible worlds (such as "I believe that lweety is unlikely to fly"). We then address the issue of ascribing semantics to first-order conditional logic. As in the propositional case, there are many possible semantics.