Fundamentals and logical foundations of truth maintenance

Abstract: "Despite their importance in AI problem solving, nonmonotonic truth maintenance systems (TMSs) still lack sufficiently well-understood logical foundations. In this thesis, I present a rigorous logical theory of TMSs. I pursue a two-step, bottom-up approach. First, I specify a direct, but implementation-independent, theory of truth maintenance. This theory, then, is used to 1) draw a connection between TMSs and Autoepistemic Logic, thus closing a gap between theory and implementation in Nonmonotonic Reasoning, 2) provide a correctness proof for an encoding of nonmonotonic justifications in an essentially monotonic assumption-based TMS, 3) design a uniform framework for truth maintenance and nonmonotonic inference based on the concept of justification-schemata, 4) discuss a model theory of TMSs in terms of stable, maximally preferred model sets. At the time of writing, no comprehensive introductory readings on truth maintenance are available. Therefore, the present thesis begins with a set of lecture notes which provide the necessary background information for the subsequent formal treatment of foundational issues."