A Critical Reexamination of Default Logic, Autoepistemic Logic, and Only Knowing

@article{Halpern1993ACR,
  title={A Critical Reexamination of Default Logic, Autoepistemic Logic, and Only Knowing},
  author={Joseph Y. Halpern},
  journal={Computational Intelligence},
  year={1993},
  volume={13}
}
Fifteen years of work on nonmonotonic logic has certainly increased our understanding of the area. However, given a problem in which nonmonotonic reasoning is called for, it is far from clear how one should go about modeling the problem using the various approaches. We explore this issue in the context on two of the best–known approaches, Reiter's default logic and Moore's autoepistemic logic, as well as two related notions of “only knowing,” due to Halpern and Moses and to Levesque. In… 

Nonmonotonicity in (the Metamathematics of) Arithmetic

This paper is an attempt to bring together two separated areas of research: classical mathematics and metamathematics on the one side, non-monotonic reasoning on the other. This is done by simulating

Reiter's Default Logic Is a Logic of Autoepistemic Reasoning And a Good One, Too

TLDR
Reiter's default logic is argued to be a bette r formalization of Moore's intuitions about autoepistemic propositions than Moore's own autoepistsemic logic.

A survey of non-monotonic reasoning

TLDR
Non-monotonic reasoning originated in the field of artificial intelligence, and has become a rapidly growing area in the last decade, and this paper discusses two of the most prominent formalizations of common-sense reasoning.

A Theory of Knowledge and Ignorance for Many Agents

TLDR
The notion of only knowing introduced by Halpern and Moses to many agents and to a number of modal logics is extended and the notion is better understood in the context of K45 (or KD45), and the appropriate notion of possibility is shown.

Only-Knowing à la Halpern-Moses for Non-omniscient Rational Agents: A Preliminary Report

TLDR
The behaviour of the HM-'only knowing' approach is examined in the realm of the weak variants of stable epistemic states introduced recently by relaxing the positive or negative introspection context rules of Stalnaker's definition, in a way reminiscent of the work done in modal epistemic logic in response to the 'logical omniscience' problem.

Reasoning about only Knowing with Many Agents

TLDR
The main lesson of this paper is that these approaches to "only knowing" do have reasonable extensions to the multi-agent case, and the results show that the HM notion is better understood in the context of K45.

Stable Belief Sets Revisited

TLDR
This paper varies the context rules underlying the positive and/or negative introspection conditions in the original definition of R. Stalnaker stable sets to obtain variant notions of a stable epistemic state, which appear to be more plausible under the epistemic viewpoint.

On the projection problem in active knowledge bases with incomplete information

TLDR
This thesis investigates the computational properties of a number of unsolved reasoning tasks in the context of projection with incomplete information, and shows that when the initial KB is an arbitrary first-order theory, conditions under which projection can be solved are identified.

Belief Revision: A Critique

TLDR
It is argued that to study belief change carefully, one must be quite explicit about the “ontology” or scenario underlying the belief change process, something that has been missing in previous work, with its focus on postulates.

Many-Valued Modal Non-Monotonic Reasoning: Sequential Stable Sets and Logics with Linear Truth Spaces

TLDR
A logical investigation of many-valued modal non-monotonic reasoning in Fitting's formal framework is taken and it is shown that several attractive epistemic properties are essentially retained in the many- valued setting, esp. when focusing on a syntactically simple epistemic fragment of MV-stable sets.

References

SHOWING 1-10 OF 32 REFERENCES

All I Know: A Study in Autoepistemic Logic

  • H. Levesque
  • Philosophy, Computer Science
    Artif. Intell.
  • 1990

Cumulative Default Logic: In Defense of Nonmonotonic Inference Rules

Autoepistemic Modal Logics

TLDR
It is shown that Moore's logic is merely a special case of McDermott's logic, at least formally, and the problems that arose inMoore's logic may find a simple and uniform solution by going back to McDermott't original concept.

Semantical Considerations on Nonmonotonic Logic

On the Relation Between Default and Autoepistemic Logic

Nonmonotonic Logic II: Nonmonotonic Modal Theories

TLDR
The operator M (usually read "possible") is extended so that Mp is true whenever p is consistent with the theory, and any theorem of this form may be mvahdated if ~p ~s is added as an axiom.

Modal nonmonotonic logics: ranges, characterization, computation

Many nonmonotonic formalism, including default logic, logic programming with stable models, and autoepistemic logic, can be represented faithfully by means of modal nonmonotonic logics in the family

Ideal Introspective Belief

TLDR
This work characterize a family of ideal AE reasoners in terms of the minimal hypotheses that they can make, and the weakest and strongest reflection principles that they could have, while still maintaining the interpretation of AE logic as self-belief.

Considerations on default logics

TLDR
An alternative approach to default logic is developed in order to address the limitations of the original approach and subsequent variants and the resulting system is called constrained default logic.

Non-Monotonic Logic I