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.
Keywords Anaphora  Default Logic  Equality  Herbrand models  Indistinguishability  Rough Set Theory  Sorites  Vagueness
Categories (categorize this paper)
DOI 10.1007/s10849-008-9057-6
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,355
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A Logic for Default Reasoning.Ray Reiter - 1980 - Artificial Intelligence 13 (1-2):81-137.
Semantic Considerations on Nonmonotonic Logic.Robert C. Moore - 1985 - Artificial Intelligence 25 (1):75-94.
A Logical Framework for Default Reasoning.David Poole - 1988 - Artificial Intelligence 36 (1):27-47.

View all 13 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles


Added to PP index

Total views
43 ( #265,324 of 2,519,571 )

Recent downloads (6 months)
1 ( #407,153 of 2,519,571 )

How can I increase my downloads?


My notes