A Semantic Theory of Abstractions

ions P. Pandurang Nayak Recom Technologies, NASA Ames Research Center, MS 269-2 Moffett Field, CA 94035. nayak@ptolemy.arc.nasa.gov Alon Y. Levy AT&T Bell Laboratories AI Principles Research Department 600 Mountain Avenue, Room 2C-406 Murray Hill, NJ 07974. levy@research.att.com Abstract In this paper we present a semantic theory of abstractions based on viewing abstractions as model level mappings. This theory captures important aspects of abstractions not captured in the syntactic theory of abstractions presented by Giunchiglia and Walsh [ 1992 ] . Instead of viewing abstractions as syntactic mappings, we view abstraction as a two step process: first, the intended domain model is abstracted and then a set of (abstract) formulas is constructed to capture the abstracted domain model. Viewing and justifying abstractions as model level mappings is both natural and insightful. This basic theory yields abstractions that are weaker than the base theory. We show that abstractions that a..