Approximate well-founded semantics, query answering and generalized normal logic programs over lattices

Loyer, Yann; Straccia, Umberto

doi:10.1007/s10472-008-9099-0

Cited by 7 publications

(7 citation statements)

References 90 publications

(54 reference statements)

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“…. , B n ), where f is a computable function that is the result of combining all the connective present in the body (this same syntax can be explicitly found in [28,29,58] and it is also accepted in many other fuzzy logic programming frameworks). For instance, a program rule like p(X )←q(X , Y )& G (r(Y )| L s(Y )) can be expressed too as p(X )←@ f (q(X , Y ), r(Y ), s(Y )) whenever the single connective on its body be defined as @ f (x, y, z) x& G (y| L z).…”

Section: The Wider Class Of X-malp Programsmentioning

confidence: 99%

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Beyond multi-adjoint logic programming

Moreno

Penabad

Vázquez

2014

International Journal of Computer Mathematics

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In 'multi-adjoint logic programming', MALP in brief, each fuzzy logic program is associated with its own 'multi-adjoint lattice' for modelling truth degrees beyond the simpler case of true and false, where a large set of fuzzy connectives can be defined. On this wide repertoire, it is crucial to connect each implication symbol with a proper conjunction thus conforming constructs of the form (← i , & i ) called 'adjoint pairs', whose use directly affects both declarative and operational semantics of the MALP framework. In this work, we firstly show how the strong dependence of adjoint pairs can be largely weakened for an interesting 'sub-class' of MALP programs. Then, we reason in a similar way till conceiving a 'super-class' of fuzzy logic programs beyond MALP, which definitively drops out the need for using adjoint pairs, since the new semantics behaviour relies on much more relaxed lattices than multi-adjoint ones.

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Section: The Wider Class Of X-malp Programsmentioning

confidence: 99%

“…(3) Bi-lattices [13][14][15]28,29], tri-lattices [25] or more generally, multi-lattices [33][34][35][36][37]. (4) A set of intervals [4,16,25,30,57] and qualified domains [6,49,50].…”

Section: Introductionmentioning

confidence: 99%

Beyond multi-adjoint logic programming

Moreno

Penabad

Vázquez

2014

International Journal of Computer Mathematics

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“…This operator allows for a better approximation of answer sets without spending too many resources. A similar idea was studied by Loyer and Straccia (2009), where a well-founded semantics is used for querying fuzzy logic programs over the Gödel t-norm. A well-founded semantics was also defined by Damásio and Pereira (2001), for which we can prove the following result.…”

Section: Corollarymentioning

confidence: 99%

Fuzzy answer sets approximations

Alviano¹,

Peñaloza²

2013

Theory and Practice of Logic Programming

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Fuzzy answer set programming (FASP) is a recent formalism for knowledge representation that enriches the declarativity of answer set programming by allowing propositions to be graded. To now, no implementations of FASP solvers are available and all current proposals are based on compilations of logic programs into different paradigms, like mixed integer programs or bilevel programs. These approaches introduce many auxiliary variables which might affect the performance of a solver negatively. To limit this downside, operators for approximating fuzzy answer sets can be introduced: Given a FASP program, these operators compute lower and upper bounds for all atoms in the program such that all answer sets are between these bounds. This paper analyzes several operators of this kind which are based on linear programming, fuzzy unfounded sets and source pointers. Furthermore, the paper reports on a prototypical implementation, also describing strategies for avoiding computations of these operators when they are guaranteed to not improve current bounds. The operators and their implementation can be used to obtain more constrained mixed integer or bilevel programs, or even for providing a basis for implementing a native FASP solver. Interestingly, the semantics of relevant classes of programs with unique answer sets, like positive programs and programs with stratified negation, can be already computed by the prototype without the need for an external tool.

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“…Manyvalued logics have been extended and applied in many fields, e.g., Kleene's three-valued logic is used in [74] for representing and reasoning with temporal information, and a new symbolic approach to representation of imprecise (or fuzzy) information has been proposed in [10] based on a symbolic many-valued logic. A more complete list of categorized references for the management of imperfect information can be found in [62,93].…”

Section: Models Based On Non-standard Logicsmentioning

confidence: 99%

On the combination of logical and probabilistic models for information analysis

et al. 2011

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Formal logical tools are able to provide some amount of reasoning support for information analysis, but are unable to represent uncertainty. Bayesian network tools represent probabilistic and causal information, but in the worst case scale as poorly as some formal logical systems and require specialized expertise to use effectively. We describe a framework for systems that incorporate the advantages of both Bayesian and logical systems. We define a formalism for the conversion of automatically generated natural deduction proof trees into Bayesian networks. We then demonstrate that the merging of such networks with domain-specific causal models forms a consistent Bayesian network with correct values for the formulas derived in the proof. In particular, we show that hard evidential updates in which the premises of a proof are found to be true force the conclusions of the proof to be true with probability one, regardless of any dependencies and prior probability values assumed for the causal model. We provide several examples that demonstrate the generality of the natural deduction system by using inference schemes not supportable directly in Horn clause logic. We compare our approach to other ones, including some that use non-standard logics.

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Approximate well-founded semantics, query answering and generalized normal logic programs over lattices

Cited by 7 publications

References 90 publications

Beyond multi-adjoint logic programming

Beyond multi-adjoint logic programming

Fuzzy answer sets approximations

On the combination of logical and probabilistic models for information analysis

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