One head is better than two: a polynomial restriction for propositional definite Horn forgetting

Logical forgetting is NP-complete even in the simple case of propositional Horn formulae. An algorithm previously introduced is improved by changing the input formula before running it. This enlarges the restriction that makes the algorithm polynomial and decreases its running time in other cases. The size of the resulting formula decreases consequently.

[1]  Bae.  50 % , 2018, CME.

[2]  Yi Zhou,et al.  Bounded Forgetting , 2011, AAAI.

[3]  Peter L. Hammer,et al.  Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression , 1995, IEEE Trans. Knowl. Data Eng..

[4]  Boris Konev,et al.  Forgetting and Uniform Interpolation in Extensions of the Description Logic EL , 2009, Description Logics.

[5]  Hector J. Levesque,et al.  Forgetting in Action , 2014, KR.

[6]  Matthias Knorr,et al.  The Ultimate Guide to Forgetting in Answer Set Programming , 2016, KR.

[7]  James M. Crawford,et al.  Experimental Results on the Crossover Point inSatis ability , 1993 .

[8]  Andreas Herzig,et al.  Introspective Forgetting , 2008, Australasian Conference on Artificial Intelligence.

[9]  Judy Goldsmith,et al.  New Horn Revision Algorithms , 2005, J. Mach. Learn. Res..

[10]  Kewen Wang,et al.  Forgetting for Defeasible Logic , 2012, LPAR.

[11]  G. Boole.  An Investigation of the Laws of Thought: On which are founded the mathematical theories of logic and probabilities , 2007 .

[12]  Christopher Umans.  The minimum equivalent DNF problem and shortest implicants , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[13]  Endre Boros,et al.  Horn minimization by iterative decomposition , 1998, Annals of Mathematics and Artificial Intelligence.

[14]  Olivier Coudert,et al.  Two-level logic minimization: an overview , 1994, Integr..

[15]  Paolo Liberatore.  Common equivalence and size after forgetting , 2020, ArXiv.

[16]  Tiziano Villa,et al.  Complexity of two-level logic minimization , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[17]  Yi Zhou,et al.  Knowledge Forgetting in Answer Set Programming , 2014, J. Artif. Intell. Res..

[18]  Paolo Liberatore,et al.  Reconstructing a single-head formula to facilitate logical forgetting , 2020, ArXiv.

[19]  Fred L. Drake,et al.  The Python Language Reference Manual , 1999 .

[20]  O. Coudert,et al.  Two-level logic minimization , 2001 .

[21]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[22]  James P. Delgrande,et al.  A Knowledge Level Account of Forgetting , 2017, J. Artif. Intell. Res..

[23]  Yves Moinard,et al.  Forgetting Literals with Varying Propositional Symbols , 2007, J. Log. Comput..

[24]  Hans Tompits,et al.  Forgetting in Managing Rules and Ontologies , 2006, 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06).

[25]  George Boole,et al.  An Investigation of the Laws of Thought: Frontmatter , 2009 .

[26]  Fangzhen Lin,et al.  Forgetting and Update -- an exploration , 2007, Formal Models of Belief Change in Rational Agents.

[27]  Esra Erdem,et al.  Forgetting Actions in Domain Descriptions , 2007, AAAI.