Semantical considerations on nonmonotonic logic
Artificial Intelligence
Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Motivation analysis, abductive unification, and nonmonotonic equality
Artificial Intelligence
A logical framework for default reasoning
Artificial Intelligence
A comparative study of open default theories
Artificial Intelligence
A note on the stable model semantics for logic programs
Artificial Intelligence
Rules in incomplete information systems
Information Sciences: an International Journal
Equality and Domain Closure in First-Order Databases
Journal of the ACM (JACM)
First-order non-monotonic modal logics
Fundamenta Informaticae
Foundations of Logic Programming
Foundations of Logic Programming
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
Journal of Automated Reasoning
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We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter's Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive "flavor." The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper.