Notions of sameness by default and their application to anaphora, vagueness, and uncertain reasoning
Journal of Logic, Language and Information 17 (3) (2008)
|Abstract||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||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Yao-Hua Tan (1997). Is Default Logic a Reinvention of Inductive-Statistical Reasoning? Synthese 110 (3):357-379.
Alex Lascarides, Ted Briscoe, Nicholas Asher & Ann Copestake (1996). Order Independent and Persistent Typed Default Unification. Linguistics and Philosophy 19 (1):1 - 90.
Gregory Wheeler & Carlos Damasio (2004). An Implementation of Statistical Default Logic. In Jose Alferes & Joao Leite (eds.), Logics in Artificial Intelligence (JELIA 2004). Springer.
G. Aldo Antonelli (1999). A Directly Cautious Theory of Defeasible Consequence for Default Logic Via the Notion of General Extension. Artificial Intelligence 109 (1-2):71-109.
Francis Jeffry Pelletier & Renée Elio (2005). The Case for Psychologism in Default and Inheritance Reasoning. Synthese 146 (1-2):7 - 35.
Gianni Amati, Luigia Carlucci Aiello & Fiora Pirri (1994). Defaults as Restrictions on Classical Hilbert-Style Proofs. Journal of Logic, Language and Information 3 (4):303-326.
Joeri Engelfriet & Jan Treur (1998). An Interpretation of Default Logic in Minimal Temporal Epistemic Logic. Journal of Logic, Language and Information 7 (3):369-388.
Beihai Zhou & Yi Mao (2006). A Base Logic for Default Reasoning. Frontiers of Philosophy in China 1 (4):688-709.
Added to index2009-01-28
Total downloads7 ( #134,983 of 556,888 )
Recent downloads (6 months)1 ( #64,931 of 556,888 )
How can I increase my downloads?