Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach

by Jeroen Janssen, Steven Schockaert, Dirk Vermeir

Answer set programming (ASP) is a declarative language tailored towards solving combinatorial optimization problems. It has been successfully applied to e.g. planning problems, configuration and verification of software, diagnosis and database repairs. However, ASP is not directly suitable for modeling problems with continuous domains. Such problems occur naturally in diverse fields such as the design of gas and electricity networks, computer vision and investment portfolios. To overcome this problem we study FASP, a combination of ASP with fuzzy logic -- a class of manyvalued logics that can handle continuity. We specifically focus on the following 1. An important question when modeling continuous optimization problems is how we should handle overconstrained problems, i.e. problems that have no solutions. In many cases we can opt to accept an imperfect solution, i.e. a solution that does not satisfy all the stated rules (constraints). However, this leads to the what imperfect solutions should we choose? We investigate this question and improve upon the state-of-the-art by proposing an approach based on aggregation functions. 2. Users of a programming language often want a rich language that is easy to model in. However, implementers and theoreticians prefer a small language that is easy to implement and reason about. We create a bridge between these two desires by proposing a small core language for FASP and by showing that this language is capable of expressing many of its common extensions such as constraints, monotonically decreasing functions, aggregators, S-implicators and classical negation. 3. A well-known technique for solving ASP consists of translating a program P to a propositional theory whose models exactly correspond to the answer sets of P. We show how this technique can be generalized to FASP, paving the way to implement efficient fuzzy answer set solvers that can take advantage of existing fuzzy reasoners.

184 pages, Hardcover

First published May 3, 2012

About the author

◦Jeroen Janssen (1963) is comic artist, illustrator and colorist.
◦Jeroen Janssen studied at the Saint-Luc art institute in Ghent.
◦He began drawing comics while living and working as an art teacher in Nyundo, Rwanda, from 1990 to 1994.
◦His first long comic story, 'Muzungu, Sluipend Gif in Rwanda', was published by Wonderland in Hasselt in 1997. This book about the civil war in Rwanda received the VSB-award during the Haarlem comics festival of in 1998.
◦Janssen made most of his following books with writer Pieter van Oudheusden, who was in the jury of the VSB Award. After the graphic novel 'Een Nachtegaal in de Stad' (1999) and the story collection 'Klaarlichte Nacht' (2001), Janssen and Van Oudheusden drew inspiration from fables and African folktales for 'Bakamé' (2003), 'De Grote Tovenaar: De kruisweg van Mpyisi' (2007) and 'De Wraak van Bakamé' (2010).
◦In 2013, Janssen made an drawn report on 'Doel', a Flemish ghosttown that is threatened with complete demolition due to the planned enlargement of the harbour of Antwerp.
◦Short stories by Janssen have appeared in magazines like Beeldstorm, Stripburger, Incognito, Kerozene, Parcifal, Ink and Zone 5300. He works part-time in a library, is freelance illustrator and does the coloring of 'Hippo & Zeno', a comic by Klaas Verplancke.
◦In 2016 a new book came out: "Abadaringi"the story of the people who were in the Art School of Nyundo (Rwanda) when he taught there in the years before the Rwandan genocide.
◦2018: a new book about Doel comes out: "Er wonen nog mensen / tekenen van leven in Doel"
◦2018: Jeroen Janssen receives the "Bronzen Adhemar" award for his entire work.