We suggest a new representation of defeasible entailment and specificity in the framework of default logic. The representation is based on augmenting the underlying classical language with the language of conditionals having its own (monotonic) internal logic. It is shown, in particular, that inheritance reasoning can be naturally represented in this framework, and generalized to the full classical language.
We suggest a new representation of defeasible entailment and specificity in the framework of default logic. The representation is based on augmenting the underlying classical language with the language of conditionals having its own (monotonic) internal logic. It is shown, in particular, that nonmonotonic inheritance reasoning can be naturally represented in this framework, and generalized to the full classical language. The problem of nonmonotonic, defeasible inference can be seen as the main objective, as well as the main problem of the general theory of nonmonotonic reasoning. An impressive success has been achieved in our understanding of it, in realizing how complex it is, and, most importantly, how many different forms it may have. Many formalisms have been developed and implemented that capture significant aspects of defeasible inference, though a unified picture has not yet emerged. In this study we will suggest a new representation of defeasible inference in the framework of default logic. As the reader will see, however, the suggested representation will borrow the main insights of many previous approaches to this problem, hopefully without inheriting their shortcomings. Preliminary version of this paper has appeared as (Bochman 2007), though in the present study we suggest a somewhat different, more transparent formalization.
We investigate defeasible logics using a technique which decomposes the semantics of such logics into two parts: a specification of the structure of defeasible reasoning and a semantics for the metalanguage in which the specification is written. We show that Nute's Defeasible Logic corresponds to Kunen's semantics, and develop a defeasible logic from the well-founded semantics of Van Gelder, Ross and Schlipf. We also obtain a new defeasible logic which extends an existing language by modifying the specification of Defeasible Logic. Thus our approach is productive in analysing, comparing and designing defeasible logics.
Recently, much attention has focused on discrepancies between intuition and formalization in nonmonotonic reasoning systems, particularly with respect to the frame problem. For example, in the Hanks-McDermott shooting problem [Hanks and McDermott, 19861, a seemingly natural formalization in terms of Reiter's Default Logic [Reiter, 19801, using normal defaults, supports two interpretations of the events where only one appears to make intuitive sense. A partial solution to this quandary is proposed in [Morris, 19871, where it is shown that a very similar formulation using a truth maintenance system (TMS) supports only the intuitively sanctioned interpretation. Moreover, that interpretation is appropriately revised in response to new conflicting information by the mechanism of dependency-directed backtracking. One drawback of the TMS solution is that truth maintenance is quite limited as an inference mechanism. For example, it is not possible, given justifications A B and -A --, B, to conclude B. It is of interest to learn to what extent the inference methods of more powerful logic systems are compatible with intuitively sound nonmonotonic reasoning.
We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be modular, in the sense that they also work if applied only to part of a theory, in order to achieve a useful notion of relative expressiveness. We present simulations showing that logics in DL with and without the capability of team defeat are equally expressive. We also show that logics that handle ambiguity differently -- ambiguity blocking versus ambiguity propagating -- have distinct expressiveness, with neither able to simulate the other under a different formulation of expressiveness.