Dynamic Reasoning Systems

A dynamic reasoning system (DRS) is an adaptation of a conventional formal logical system that explicitly portrays reasoning as a temporal activity, with each extralogical input to the system and each inference rule application being viewed as occurring at a distinct timestep. Every DRS incorporates some well-defined logic together with a controller that serves to guide the reasoning process in response to user inputs. Logics are generic, whereas controllers are application specific. Every controller does, nonetheless, provide an algorithm for nonmonotonic belief revision. The general notion of a DRS comprises a framework within which one can formulate the logic and algorithms for a given application and prove that the algorithms are correct, that is, that they serve to (1) derive all salient information and (2) preserve the consistency of the belief set. This article illustrates the idea with ordinary first-order predicate calculus, suitably modified for the present purpose, and two examples. The latter example revisits some classic nonmonotonic reasoning puzzles (Opus the Penguin, Nixon Diamond) and shows how these can be resolved in the context of a DRS, using an expanded version of first-order logic that incorporates typed predicate symbols. All concepts are rigorously defined and effectively computable, thereby providing the foundation for a future software implementation.

[1]  Thomas Andreas Meyer,et al.  Semantic Foundation for Preferential Description Logics , 2011, Australasian Conference on Artificial Intelligence.

[2]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[3]  Eduardo L. Fermé,et al.  Belief Revision , 2007, Inteligencia Artif..

[4]  José Júlio Alferes,et al.  LUPS - A Language for Updating Logic Programs , 1999, LPNMR.

[5]  Daniel G. Schwartz,et al.  Formal Specifications for a Document Management Assistant , 2009, SCSS.

[6]  José Júlio Alferes,et al.  Dynamic Logic Programming , 1998, APPIA-GULP-PRODE.

[7]  Daniel Lehmann,et al.  Another perspective on default reasoning , 1995, Annals of Mathematics and Artificial Intelligence.

[8]  Chitta Baral,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2003 .

[9]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[10]  Donald Perlis,et al.  LIFE ON A DESERT ISLAND: ONGOING WORK ON REAL-TIME REASONING , 1987 .

[11]  Marvin Minsky,et al.  A framework for representing knowledge" in the psychology of computer vision , 1975 .

[12]  Yoav Shoham,et al.  Agent-Oriented Programming , 1992, Artif. Intell..

[13]  Lynn Andrea Stein,et al.  Resolving Ambiguity in Nonmonotonic Inheritance Hierarchies , 1992, Artif. Intell..

[14]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[15]  Y. Shoham.  Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence , 1987 .

[16]  Elliott Mendelson,et al.  Introduction to mathematical logic (3. ed.) , 1987 .

[17]  G. Hegel.  The Phenomenology of Mind , 1932, Nature.

[18]  P. Hayes.  The Logic of Frames , 1981 .

[19]  Y. Shoham,et al.  Temporal reasoning in artificial intelligence , 1988 .

[20]  Barbara M. Smith,et al.  Reason maintenance systems and their applications , 1988 .

[21]  Sven Ove Hansson,et al.  A textbook of belief dynamics - theory change and database updating , 1999, Applied logic series.

[22]  Daniel G. Schwartz,et al.  Algorithms for Maintaining a Consistent Knowledge Base in Distributed Multiagent Environments , 2009, SCSS.

[23]  Michael Gelfond,et al.  Knowledge Representation, Reasoning, and the Design of Intelligent Agents: The Answer-Set Programming Approach , 2014 .

[24]  Daniel G. Schwartz,et al.  Dynamic agent-oriented reasoning about belief and trust , 2008, Multiagent Grid Syst..

[25]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[26]  Ivan José Varzinczak,et al.  On Action Theory Change , 2014, J. Artif. Intell. Res..

[27]  Peter G¿rdenfors,et al.  Belief Revision , 2003 .

[28]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

[29]  Donald Perlis,et al.  Stop the world—I want to think , 1990, Int. J. Intell. Syst..

[30]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[31]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[32]  Alonzo Church,et al.  A note on the Entscheidungsproblem , 1936, Journal of Symbolic Logic.

[33]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[34]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[35]  Peter Gärdenfors,et al.  Belief Revision: Contents , 1992 .

[36]  Matthew L. Ginsberg,et al.  Readings in Nonmonotonic Reasoning , 1987, AAAI 1987.

[37]  David S. Touretzky,et al.  Implicit Ordering of Defaults in Inheritance Systems , 1984, AAAI.

[38]  Donald Perlis,et al.  Step-logic: reasoning situated in time , 1988 .

[39]  Yoav Shoham,et al.  Chronological Ignorance: Time, Nonmonotonicity, Necessity and Causal Theories , 1986, AAAI.

[40]  Michael Miller,et al.  Memory, Reason, and Time: the Step-logic Approach , 1991 .

[41]  Ivan Jos.  On Action Theory Change , 2010 .

[42]  José Júlio Alferes,et al.  Multi-dimensional Dynamic Knowledge Representation , 2001, LPNMR.

[43]  Mikolás Janota,et al.  Digital Object Identifier (DOI): , 2000 .

[44]  Michael J. Miller.  A view of one's past and other aspects of reasoned change in belief , 1993 .

[45]  Donald Perlis,et al.  Reasoning situated in time I: basic concepts , 1990, J. Exp. Theor. Artif. Intell..

[46]  Daniel G. Schwartz,et al.  Architecture for Belief Revision in Multi-Agent Intelligent Systems , 2008 .

[47]  Juliane Hahn,et al.  The Critique Of Pure Reason , 2016 .

[48]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[49]  Thomas Eiter,et al.  Updating action domain descriptions☆ , 2005, IJCAI.

[50]  Peter Gärdenfors,et al.  Knowledge in Flux: Modeling the Dynamics of Epistemic States , 2008 .

[51]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[52]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

[53]  Elliott Mendelson.  Introduction to Mathematical Logic, Third Edition , 1987 .

[54]  S. Hansson,et al.  Twenty-Five Years of Research in Belief Change , 2011 .

[56]  Daniel G. Schwartz,et al.  Multiagent dynamic reasoning about belief and trust , 2008 .

[57]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[58]  J. McCarthy.  Circumscription|a Form of Nonmonotonic Reasoning , 1979 .

[59]  Jon Doyle,et al.  A Truth Maintenance System , 1979, Artif. Intell..

[60]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[61]  David S. Touretzky,et al.  A Clash of Intuitions: The Current State of Nonmonotonic Multiple Inheritance Systems , 1987, IJCAI.

[62]  Daniel G. Schwartz,et al.  Dynamic Reasoning with Qualified Syllogisms , 1997, Artif. Intell..

[63]  C. E. Alchourrón,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985 .

[64]  R. Reiter,et al.  Forget It ! , 1994 .

[65]  José Júlio Alferes,et al.  Dynamic updates of non-monotonic knowledge bases , 2000, J. Log. Program..

[66]  José Júlio Alferes,et al.  The Refined Extension Principle for Semantics of Dynamic Logic Programming , 2005, Stud Logica.