Negation as a Resource: A Novel View on Answer Set Semantics

In recent work, we provided a formulation of ASP programs in terms of linear logic theories. Based on this work, in this paper we propose and discuss a modified Answer Set Semantics, "Resource-based Answer Set Semantics".

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

[2]  Max I. Kanovich,et al.  The Complexity of Horn Fragments of Linear Logic , 1994, Ann. Pure Appl. Log..

[3]  Luís Moniz Pereira,et al.  Tight Semantics for Logic Programs , 2010, ICLP.

[4]  Stefania Costantini,et al.  Query answering in resource-based answer set semantics* , 2016, Theory and Practice of Logic Programming.

[5]  Stefania Costantini,et al.  Answer Set Programming with Resources , 2010, J. Log. Comput..

[6]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[7]  Jürgen Dix,et al.  A Classification Theory of Semantics of Normal Logic Programs: I. Strong Properties , 1995, Fundam. Informaticae.

[8]  Luís Moniz Pereira,et al.  Revised Stable Models - A Semantics for Logic Programs , 2005, EPIA.

[9]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[10]  Stefania Costantini,et al.  Contributions to the Stable Model Semantics of Logic Programs with Negation , 1993, Theor. Comput. Sci..

[11]  Grigori Schwarz.  Reflexive Autoepistemic logic , 1992, Fundam. Informaticae.

[12]  Ilkka Niemelä,et al.  Stable Model Semantics of Weight Constraint Rules , 1999, LPNMR.

[13]  Max J. Cresswell,et al.  A companion to modal logic , 1984 .

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

[15]  Jean-Yves Girard,et al.  Linear logic: its syntax and semantics , 1995 .

[16]  Stefania Costantini,et al.  Under Consideration for Publication in Theory and Practice of Logic Programming on the Existence of Stable Models of Non-stratified Logic Programs , 2022 .

[17]  Stefania Costantini,et al.  Nested Weight Constraints in ASP , 2011, CILC.

[18]  Stefania Costantini,et al.  Augmenting Weight Constraints with Complex Preferences , 2011, AAAI Spring Symposium: Logical Formalizations of Commonsense Reasoning.

[19]  Serenella Cerrito,et al.  A Linear Axiomatization of Negation as Failure , 1992, J. Log. Program..

[20]  Michael Gelfond,et al.  On Stratified Autoepistemic Theories , 1987, AAAI.

[21]  Miroslaw Truszczynski,et al.  Extremal Problems in Logic Programming and Stable Model Computation , 1996, J. Log. Program..

[22]  Stefania Costantini,et al.  Extending and Implementing RASP , 2010, Fundam. Informaticae.

[23]  Marco Cadoli,et al.  The Complexity of Model Checking for Circumscriptive Formulae , 1992, Inf. Process. Lett..

[24]  Stefania Costantini,et al.  Modeling preferences and conditional preferences on resource consumption and production in ASP , 2009, J. Algorithms.

[25]  Mauricio Osorio,et al.  Logics with Common Weak Completions , 2006, J. Log. Comput..

[26]  Stefania Costantini,et al.  Weight Constraints with Preferences in ASP , 2011, LPNMR.

[27]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[28]  Georg Gottlob,et al.  Complexity and expressive power of logic programming , 2001, CSUR.

[29]  Vladimir Lifschitz,et al.  Twelve Definitions of a Stable Model , 2008, ICLP.

[30]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[31]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

[32]  Victor W. Marek,et al.  Nonmonotonic logic - context-dependent reasoning , 1997, Artificial intelligence.

[33]  Miroslaw Truszczynski.  Logic Programming for Knowledge Representation , 2007, ICLP.

[34]  Robert E. Mercer,et al.  Monotonic Answer Set Programming , 2009, J. Log. Comput..

[35]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[36]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[37]  Grigori Schwarz.  Autoepistemic Logic of Knowledge , 1991, LPNMR.

[38]  Mauricio Osorio,et al.  Expressing the Stable Semantics in Terms of the Pstable Semantics , 2006, LoLaCOM.

[39]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[40]  Nicola Leone.  Logic Programming and Nonmonotonic Reasoning: From Theory to Systems and Applications , 2007, LPNMR.

[41]  Stefania Costantini,et al.  RASP and ASP as a fragment of linear logic , 2013, J. Appl. Non Class. Logics.

[42]  Krzysztof R. Apt,et al.  Logic Programming and Negation: A Survey , 1994, The Journal of Logic Programming.

[43]  Miroslaw Truszczynski,et al.  Answer Set Optimization , 2003, IJCAI.

[44]  Fangzhen Lin,et al.  On Odd and Even Cycles in Normal Logic Programs , 2004, AAAI.

[45]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[46]  Kurt Konolige,et al.  On the Relation Between Default and Autoepistemic Logic , 1987, Artif. Intell..