Comparing formal theories of context in AI

The problem of context has a long tradition in different areas of artificial intelligence (AI). However, formalizing context has been widely discussed only since the late 80s, when J. McCarthy argued that formalizing context was a crucial step toward the solution of the problem of generality. Since then, two main formalizations have been proposed in AI: Propositional Logic of Context (PLC) and Local Models Semantics/MultiContext Systems (LMS/MCS). In this paper, we propose the first in depth comparison between these two formalizations, both from a technical and a conceptual point of view. The main technical result of this paper is the formal proof of the following facts: (i) PLC can be embedded into a particular class of MCS, called MPLC; (ii) MCS/LMS cannot be embedded in PLC using only lifting axioms to encode bridge rules, and (iii) under some important restrictions (including the hypothesis that each context has finite and homogeneous propositional languages), MCS/LMS can be embedded in PLC with generic axioms. The last part of the paper contains a comparison of the epistemological adequacy of PLC and MCS/LMS for the representation of the most important issues about contexts.

[1]  Luciano Serafini,et al.  Proceedings of the 2nd International and Interdisciplinary Conference on Modeling and Using Context, CONTEXT-99 , 1999 .

[2]  Varol Akman,et al.  Steps Toward Formalizing Context , 1996, AI Mag..

[3]  Yukio Murakoshi.  Indexicals and Demonstratives : Fregean and Anti-Fregean Accounts of the Relation between Reference and Sense , 1995 .

[4]  R. Guha.  Contexts: a formalization and some applications , 1992 .

[5]  Fausto Giunchiglia,et al.  Reasoning about Theory Adequacy. A New Solution to the Qualification Problem , 1995, Fundam. Informaticae.

[6]  John McCarthy,et al.  Generality in artificial intelligence , 1987, Resonance.

[7]  Pattie Maes,et al.  Meta-Level Architectures and Reflection , 1988 .

[8]  Fausto Giunchiglia,et al.  A Foundation for Metareasoning Part I: The Proof Theory , 2002, J. Log. Comput..

[9]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

[10]  David Kaplan,et al.  On the logic of demonstratives , 1979, J. Philos. Log..

[11]  Y. Bar-Hillel.  V.—INDEXICAL EXPRESSIONS , 1954 .

[12]  Fausto Giunchiglia,et al.  A Foundation for Metareasoning Part II: The Model Theory , 2002, J. Log. Comput..

[13]  Vladimir Lifschitz,et al.  Formalizing Common Sense: Papers by John McCarthy , 1998 .

[14]  Fausto Giunchiglia,et al.  Multilanguage hierarchical logics (or: how we can do without modal logics) , 1994, CNKBS.

[15]  Fausto Giunchiglia,et al.  Contextual Reasoning , 1998, ECAI.

[16]  Fausto Giunchiglia,et al.  What is Local Models Semantics , 2002 .

[17]  Richmond H. Thomason.  Type Theoretic Foundations for Context, Part 1: Contexts as Complex Type-Theoretic Objects , 1999, CONTEXT.

[18]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[19]  Patrick Brézillon,et al.  Context in problem solving: a survey , 1999, The Knowledge Engineering Review.

[20]  Attach Ptheorem.  A Multi-Context Monotonic Axiomatization of Inessential Non-Monotonicity , 1988 .

[21]  Varol Akman,et al.  Modeling Context with Situations , 1995 .

[22]  Jon Barwise,et al.  On Conditionals: CONDITIONALS AND CONDITIONAL INFORMATION , 1986 .

[23]  Sasa Buvac.  Quantificational Logic of Context , 1996, AAAI/IAAI, Vol. 1.

[24]  Fausto Giunchiglia,et al.  Local Models Semantics, or Contextual Reasoning = Locality + Compatibility , 1998, KR.

[25]  Fausto Giunchiglia,et al.  Introduction to Contextual Reasoning. An Artificial Intelligence Perspective , 1997 .

[26]  John Dinsmore.  A Logic of Partitioned Representations , 1991 .

[27]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[28]  J. McCarthy,et al.  Formalizing Context (Expanded Notes) , 1994 .

[29]  Ian A. Mason,et al.  Metamathematics of Contexts , 1995, Fundam. Informaticae.

[30]  Gilles Fauconnier,et al.  Mental Spaces: Aspects of Meaning Construction in Natural Language , 1985 .

[31]  Richard W. Weyhrauch,et al.  Prolegomena to a Theory of Mechanized Formal Reasoning , 1980, Artif. Intell..

[32]  John McCarthy,et al.  Notes on Formalizing Context , 1993, IJCAI.