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**1 - 4**of**4**### Towards Possibilistic Fuzzy Answer Set Programming

"... Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. ..."

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Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

### Under consideration for publication in Theory and Practice of Logic Programming 1 Stable Model Semantics for Founded Bounds

, 2003

"... 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 p ..."

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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.

### Under consideration for publication in Theory and Practice of Logic Programming 1 Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics

"... In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy l ..."

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In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of clas-sical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy answer set programming solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners. To appear in Theory and Practice of Logic Programming (TPLP).

### A core language for fuzzy answer set programming

"... A number of different Fuzzy Answer Set Programming (FASP) formalisms have been proposed in the last years, which all differ in the language extensions they support. In this paper we investigate the expressivity of these frameworks. Specifically we show how a variety of constructs in these languages ..."

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A number of different Fuzzy Answer Set Programming (FASP) formalisms have been proposed in the last years, which all differ in the language extensions they support. In this paper we investigate the expressivity of these frameworks. Specifically we show how a variety of constructs in these languages can be implemented using a considerably simpler core language. These simulations are important as a compact and simple language is easier to implement and to reason about, while an expressive language offers more options when modeling problems.