Get Answer Set Programming for Continuous Domains: A Fuzzy Logic PDF

By Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock

ISBN-10: 9491216589

ISBN-13: 9789491216589

Solution set programming (ASP) is a declarative language adapted in the direction of fixing combinatorial optimization difficulties. it's been effectively utilized to e.g. making plans difficulties, configuration and verification of software program, prognosis and database maintenance. besides the fact that, ASP isn't really without delay appropriate for modeling issues of non-stop domain names. Such difficulties ensue evidently in different fields similar to the layout of gasoline and electrical energy networks, laptop imaginative and prescient and funding portfolios. to beat this challenge we research FASP, a mixture of ASP with fuzzy common sense -- a category of manyvalued logics which can deal with continuity. We in particular concentrate on the next concerns: 1. a huge query while modeling non-stop optimization difficulties is how we should always deal with overconstrained difficulties, i.e. difficulties that experience no options. in lots of situations we will choose to settle for a less than perfect answer, i.e. an answer that doesn't fulfill the entire said ideas (constraints). besides the fact that, this ends up in the query: what imperfect recommendations may still we decide? We examine this query and enhance upon the cutting-edge via offering an method in line with aggregation capabilities. 2. clients of a programming language frequently desire a wealthy language that's effortless to version in. in spite of the fact that, implementers and theoreticians favor a small language that's effortless to enforce and cause approximately. We create a bridge among those wants via featuring a small middle language for FASP and via displaying that this language is in a position to expressing a lot of its universal extensions reminiscent of constraints, monotonically lowering capabilities, aggregators, S-implicators and classical negation. three. a well known strategy for fixing ASP contains translating a software P to a propositional idea whose versions precisely correspond to the reply units of P. We express how this method could be generalized to FASP, paving how you can enforce effective fuzzy solution set solvers which could make the most of present fuzzy reasoners.

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Extra info for Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach

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Consider the following input rules I from [Babovich et al. (2000)]: vertex(v0 ) ← vertex(v1 ) ← edge(v0 , v0 ) ← edge(v1 , v1 ) ← The grounded program gnd(Pgc ∪I) will have no answer sets, as no Hamilton cycle exists in this graph. The set {vertex(v0 ), vertex(v1 ), edge(v0 , v0 ), edge(v1 , v1 ), in(v0 , v0 ), in(v1 , v1 ), reachable(v0 ), reachable(v1 )} is a model of comp(gnd(Pgc ) ∪ I), however. 3 Fuzzy Logic In this section we introduce fuzzy sets and fuzzy logic. 3. 1 Answer Set Programming for Continuous Domains:a Fuzzy Logic Approach Fuzzy Sets We briefly introduce the concepts from fuzzy set theory that we will use throughout this book.

The GL transformation then essentially replaces such literals with their values in the intended stable model interpretation, yielding a positive program. The semantics of a FASP program can now be defined in terms of the semantics of the positive reduct program. 8. Let P be a FASP program. An interpretation A of P is an answer set of P iff A is the answer set of PA . Note that, in the boolean case, the idea of negation-as-failure is that not a is true for an atom a if during the application of forward chaining we fail to establish the truth of a.

Hence the set of axioms is countable, but not finite. The deduction rule, theories, proofs, provability and models are defined as for Łukasiewicz logic. Finally, reasoning in the above logics can be done using existing methods. For G¨odel logic we can use boolean SAT solvers, for Łukasiewicz and rational Pavelka logic we can use mixed integer programming (MIP) [H¨ahnle (1994)] or constraint satisfaction [Schockaert et al. (2009)] and for product logic we can use bounded mixed integer quadratically constrained programming (bMICQP), as is used for fuzzy description logics [Bobillo and Straccia (2007)].

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Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach by Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock

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