Rule Calculus: Semantics, Axioms and Applications

We consider the problem of how a default rule can be deduced from a default theory. For this purpose, we propose an axiom system which precisely captures the deductive reasoning about default rules. We show that our axiomatic system is sound and complete under the semantics of the logic of here-and-there. We also study other important properties such as substitution and monotonicity of our system and prove the essential decision problem complexity. Finally, we discuss applications of our default rule calculus to various problems.

[1]  Nicola Olivetti,et al.  A Sequent Calculus for Skeptical Default Logic , 1997, TABLEAUX.

[2]  Georg Gottlob,et al.  Complexity Results for Nonmonotonic Logics , 1992, J. Log. Comput..

[3]  Hector Geffner,et al.  Conditional Entailment: Bridging two Approaches to Default Reasoning , 1992, Artif. Intell..

[4]  Marianne Winslett,et al.  Updating logical databases , 1990, Cambridge tracts in theoretical computer science.

[5]  Gordon Plotkin,et al.  A Note on Inductive Generalization , 2008 .

[6]  Lex Hendriks,et al.  Characterization of strongly equivalent logic programs in intermediate logics , 2002, Theory and Practice of Logic Programming.

[7]  Yan Zhang,et al.  General Default Logic , 2007, LPNMR.

[8]  Jürgen Dix,et al.  Non-Monotonic Extensions of Logic Programming , 1996, Lecture Notes in Computer Science.

[9]  Pedro Cabalar,et al.  Propositional theories are strongly equivalent to logic programs , 2007, Theory Pract. Log. Program..

[10]  Chiaki Sakama,et al.  Generality and Equivalence Relations in Default Logic , 2007, AAAI.

[11]  Hudson Turner.  Strong Equivalence for Logic Programs and Default Theories (Made Easy) , 2001, LPNMR.

[12]  David Pearce,et al.  A New Logical Characterisation of Stable Models and Answer Sets , 1996, NMELP.

[13]  Alex S. Taylor,et al.  Machine intelligence , 2009, CHI.

[14]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

[15]  Paolo Ferraris,et al.  Answer Sets for Propositional Theories , 2005, LPNMR.

[16]  Ka-Shu Wong.  Sound and Complete Inference Rules for SE-Consequence , 2008, J. Artif. Intell. Res..

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

[18]  Gerhard Lakemeyer,et al.  Towards an Axiom System for Default Logic , 2006, AAAI.

[19]  Yuri Gureoich.  Intuitionistic Logic , 2008 .

[20]  M. Gelfond,et al.  Disjunctive Defaults , 1991 .

[21]  Rachel Ben-Eliyahu-Zohary.  Yet some more complexity results for default logic , 2002, Artif. Intell..

[22]  D. Gabbay,et al.  Handbook of Philosophical Logic, Volume II. Extensions of Classical Logic , 1986 .

[23]  Stefan Woltran,et al.  Simplifying Logic Programs Under Uniform and Strong Equivalence , 2004, LPNMR.

[24]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.