Fuzzy Answer Set Programming: An Introduction

Blondeel, Marjon; Schockaert, Steven; Vermeir, Dirk; Cock, Martine De

doi:10.1007/978-3-642-34922-5_15

Cited by 10 publications

(10 citation statements)

References 22 publications

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“…In contrast chuffed requires 3.6kB and less than 0.005 seconds for all instances. ASP (FASP) (Nieuwenborgh et al 2006;Blondeel et al 2013) can all be expressed directly as BFASP instances. In CASP, all rules are of the form: a ← p 1 ∧.…”

Section: Resultsmentioning

confidence: 99%

“…ASP with choice rules, weighted sum, max, min etc, (see (Calimeri et al 2013) for a recent standardization of the ASP language) are easily expressible as BFASPs. Similar, Constraint Answer Set Programming (CASP) (Gebser et al 2009) and even Fuzzy ASP (FASP) (Nieuwenborgh et al 2006;Blondeel et al 2013) can all be expressed directly as BFASP instances. In CASP, all rules are of the form: a ← p 1 ∧ .…”

Section: Related Workmentioning

confidence: 99%

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Stable model semantics for founded bounds

Aziz¹,

Chu²,

Stuckey³

2013

Theory and Practice of Logic Programming

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Answer Set Programming (ASP) is a powerful form of declarative programming used in areas such as planning or reasoning. ASP solvers enforce stable model semantics, which rule out solutions representing certain kinds of circular reasoning. Unfortunately, current ASP solvers are incapable of solving problems involving cyclic dependencies between multiple integer or continuous quantities effectively. In this paper, we generalize the notion of stable models to bound founded variables with arbitrary domains, where bounds on such variables need to be justified by some rule in the program in order for the model to be stable. We show how to handle significantly more general rule forms where bound founded variables can act as head or body variables, and where head and body variables can be related via complex constraints subject to certain monotonicity requirements. We describe a new unfounded set detection algorithm which allows us to enforce this generalization of the stable model semantics. We also show how these unfounded sets can be explained in order to allow effective conflict-directed clause learning. The new solver merges the best features of CP, SAT and ASP solvers and allows new types of problems to be solved very efficiently.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Stable model semantics for founded bounds

Aziz¹,

Chu²,

Stuckey³

2013

Theory and Practice of Logic Programming

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show abstract

“…In LRNNs where all the outputs are between 0 and 1, a natural choice for this activation function, which is in line with the semantics of several existing multi-valued logic programming frameworks (Damásio & Pereira, 2001a;Blondeel, Schockaert, Vermeir, & De Cock, 2013), is g not (x) = 1 − x. In other contexts, where positive and negative values are associated with positive and negative support, respectively, the choice g not (x) = −x could be used.…”

Section: Negation As Failurementioning

confidence: 99%

Lifted Relational Neural Networks: Efficient Learning of Latent Relational Structures

Šourek¹,

Aschenbrenner²,

Železný³

et al. 2018

jair

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We propose a method to combine the interpretability and expressive power of firstorder logic with the effectiveness of neural network learning. In particular, we introduce a lifted framework in which first-order rules are used to describe the structure of a given problem setting. These rules are then used as a template for constructing a number of neural networks, one for each training and testing example. As the different networks corresponding to different examples share their weights, these weights can be efficiently learned using stochastic gradient descent. Our framework provides a flexible way for implementing and combining a wide variety of modelling constructs. In particular, the use of first-order logic allows for a declarative specification of latent relational structures, which can then be efficiently discovered in a given data set using neural network learning. Experiments on 78 relational learning benchmarks clearly demonstrate the effectiveness of the framework.

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“…The semantics of FASP is traditionally defined on a complete truth lattice L = L, ≤ L [4]. In this paper, we consider two types of truth-lattice: the infinite-valued lattice L ∞ = [0, 1], ≤ and the finite-valued lattices for appropriate expressions α and β.…”

Section: Preliminaries 21 Fuzzy Answer Set Programmingmentioning

confidence: 99%

Solving Disjunctive Fuzzy Answer Set Programs

Mushthofa

Schockaert

Cock

2015

Logic Programming and Nonmonotonic Reasoning

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Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm which is tailored for continuous domains. Despite the existence of several prototype implementations, none of the existing solvers can handle disjunctive rules in a sound and efficient manner. We first show that a large class of disjunctive FASP programs called the self-reinforcing cycle-free (SRCF) programs can be polynomially reduced to normal FASP programs. We then introduce a general method for solving disjunctive FASP programs, which combines the proposed reduction with the use of mixed integer programming for minimality checking. We also report the result of the experimental benchmark of this method.

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Fuzzy Answer Set Programming: An Introduction

Cited by 10 publications

References 22 publications

Stable model semantics for founded bounds

Stable model semantics for founded bounds

Lifted Relational Neural Networks: Efficient Learning of Latent Relational Structures

Solving Disjunctive Fuzzy Answer Set Programs

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