Fuzzy answer set programming: from theory to practice

In this chapter, we give an introduction to Fuzzy Answer Set Programming (FASP), as well as a description of a state-of-the-art FASP solver and its use in practice. FASP is an extension of Answer Set Programming (ASP), a well known declarative language that allows users to specify combinatorial search and optimization problems in an intuitive way. By combining ASP with fuzzy logic, FASP is capable of expressing continuous optimization problems. In the chapter, we provide a high-level explanation of how ASP is typically used for solving problems, and the role that an extension to FASP can play in applications. We present the syntax and semantics of FASP, and describe how FASP programs are used to encode problems. We subsequently explain how our solver finds the answer sets of a FASP program, and we illustrate the whole workflow using an application for modeling of gene regulatory networks.

[1]  Aaron Hunter,et al.  A General Approach to the Verification of Cryptographic Protocols Using Answer Set Programming , 2009, LPNMR.

[2]  Marius Thomas Lindauer,et al.  Potassco: The Potsdam Answer Set Solving Collection , 2011, AI Commun..

[3]  Alexander Bockmayr,et al.  Bio-Logics: Logical Analysis of Bioregulatory Networks , 2013, Programming Logics.

[4]  R. Thomas,et al.  Boolean formalization of genetic control circuits. , 1973, Journal of theoretical biology.

[5]  Esra Erdem,et al.  Theory and applications of answer set programming , 2002 .

[6]  René Thomas.  Regulatory networks seen as asynchronous automata: A logical description , 1991 .

[7]  Martine De Cock,et al.  Complexity of fuzzy answer set programming under Łukasiewicz semantics , 2014, Int. J. Approx. Reason..

[8]  Mario Alviano,et al.  Fuzzy answer set computation via satisfiability modulo theories , 2015, Theory and Practice of Logic Programming.

[9]  Mario Alviano,et al.  Fuzzy answer sets approximations , 2013, Theory Pract. Log. Program..

[10]  Martine De Cock,et al.  Solving Disjunctive Fuzzy Answer Set Programs , 2015, LPNMR.

[11]  Martine De Cock,et al.  Fuzzy Answer Set Programming , 2006, JELIA.

[12]  Giovanni De Micheli,et al.  Synchronous versus asynchronous modeling of gene regulatory networks , 2008, Bioinform..

[13]  Marcelle Kaufman,et al.  Positive Feedback Circuits and Adaptive Regulations in Bacteria , 2001, Acta biotheoretica.

[14]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[15]  Martin Gebser,et al.  The BioASP Library: ASP Solutions for Systems Biology , 2010, 2010 22nd IEEE International Conference on Tools with Artificial Intelligence.

[16]  Martin D. F. Wong,et al.  Wire Routing and Satisfiability Planning , 2000, Computational Logic.

[17]  Nicola Leone,et al.  ASP at Work: Spin-off and Applications of the DLV System , 2011, Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning.

[18]  Ilkka Niemelä,et al.  The Answer Set Programming Paradigm , 2016, AI Mag..

[19]  Alex M. Andrew,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2004 .

[20]  Rina Dechter,et al.  Propositional semantics for disjunctive logic programs , 1994, Annals of Mathematics and Artificial Intelligence.

[21]  Martine De Cock,et al.  Fuzzy Answer Set Programming: An Introduction , 2013, Soft Computing: State of the Art Theory and Novel Applications.

[22]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER IN EVOLUTION: SELF-ORGANIZATION AND SELECTION , 1992 .

[23]  Martine De Cock,et al.  General Fuzzy Answer Set Programs , 2009, WILF.

[24]  Torsten Schaub,et al.  Modeling Biological Networks by Action Languages via Answer Set Programming , 2008, Constraints.

[25]  Stefan Woltran,et al.  Special issue on answer set programming , 2011, AI Commun..

[26]  C. Espinosa-Soto,et al.  A Gene Regulatory Network Model for Cell-Fate Determination during Arabidopsis thaliana Flower Development That Is Robust and Recovers Experimental Gene Expression Profilesw⃞ , 2004, The Plant Cell Online.

[27]  Kathleen Marchal,et al.  ASP-G: an ASP-based method for finding attractors in genetic regulatory networks , 2014, Bioinform..

[28]  Martine De Cock,et al.  A finite-valued solver for disjunctive fuzzy answer set programs , 2014, ECAI.

[29]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[30]  Kathleen Marchal,et al.  Modeling multi-valued biological interaction networks using fuzzy answer set programming , 2018, Fuzzy Sets Syst..

[31]  Luís Moniz Pereira,et al.  Antitonic Logic Programs , 2001, LPNMR.

[32]  Jürgen Dix,et al.  Reducing Disjunctive to Non-Disjunctive Semantics by Shift-Operations , 1996, Fundam. Informaticae.

[33]  Vladimir Lifschitz,et al.  Answer Set Programming , 2019 .