On Reachability of Minimal Models of Multilattice-Based Logic Programs

2009

Fuzzy Sets and Systems

Partial evaluation (PE) is an automatic program transformation technique aiming to obtain, among other advantages, the optimization of a program with respect to parts of its input: hence, it is also known as program specialization. This paper introduces the subject of PE into the field of fuzzy logic programming. We define the concept of PE for multi-adjoint logic programs and goals, and apart from discussing the benefits achieved by this technique, we also introduce in the fuzzy setting a completely novel application of PE which allows us the computation of reductants guaranteeing completeness properties without harming the computational efficiency. Reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties. As observed in the specialized literature, a multi-adjoint logic program, when interpreted on a partially ordered lattice, has to include all its reductants in order to preserve the (approximate) completeness property. This introduces severe penalties in the implementation of efficient multiadjoint logic programming systems: not only the size of programs increases but also their execution time. In this paper we define a refinement to the notion of reductant based on PE techniques, that we call P E-reductant. We establish the main properties of P E-reductants (i.e., the classical concept of reductant and the new notion of P E-reductant are both, semantically and operationally, equivalent) and, what is the best, we demonstrate that our refined notion of P E-reductant is even able to increase the efficiency of multi-adjoint logic programs.

Section: Final Discussionmentioning

confidence: 99%

An improved reductant calculus using fuzzy partial evaluation techniques

Julián¹,

2009

Fuzzy Sets and Systems

“…Although out of the scope of this paper, in the future we plan to analyse some canonical extensions for multi-adjoint lattices, formally introduced in [10] (see also [11,31], which study the completion of an n-ordered set) that have associated monotone operators and analyse the results especially for the habitual domains in MALP of bilattices and trilattices [4][5][6][7][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices

Morcillo

International Journal of Computer Mathematics

et al. 2012

Fuzzy logic programming tries to introduce fuzzy logic into logic programming in order to provide new generation computer languages which incorporate comfortable programming resources for helping the development of applications where uncertainty could play an important role. In this sense, the mathematical concept of multi-adjoint lattice has been successfully exploited into the so-called Multi-Adjoint Logic Programming approach, MALP in brief, for modelling flexible notions of truth-degrees beyond the simpler case of true and false. In this paper, we focus on two relevant mathematical concepts for this kind of domains useful for evaluating MALP. On the one side, we adapt the classical notion of Dedekind-MacNeille completion in order to relax some usual hypothesis on such kind of ordered sets, and next we study the advantages of generating multi-adjoint lattices as the Cartesian product of previous ones. On the practical side, we show that the formal mechanisms described before have direct correspondences with interesting debugging tasks into the 'Fuzzy Logic Programming Environment for Research', FLOPER in brief, developed in our research group.

“…(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

International Journal of Computer Mathematics

Vázquez

2014

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.