China
Africa
Explore chapters and articles related to this topic
Logic Programming and Artificial Neural Networks
Published in Pascal Hitzler, Anthony Seda, Mathematical Aspects of Logic Programming Semantics, 2016
Sebastian Bader, Pascal Hitzler, Anthony Seda
In this section, we outline the idea underlying the approach presented below. Suppose given a normal logic program P and any one of the semantic operators TP: IP – IP we have thus far associated with P, using TP and IP as generic symbols for a semantic operator and its underlying set of interpretations. For simplicity, we assume the interpretations in question are Herbrand interpretations taking values in a truth set T, although the conclusions we make here are valid over any preinterpretation J whose domain D is countable. Can one find, or at least show the existence of, a multilayer feedforward network FP which computes TP in some sense? Furthermore, can this network FP, or some other appropriate network, compute the least fixed point of TP assuming the least fixed point of TP exists?
Fuzzy Rule Languages
Published in Umberto Straccia, Foundations of Fuzzy Logic and Semantic Web Languages, 2016
A query driven procedure for equational systems. It is illustrative to address the following specific problem. Consider an equational system S = (L, V, f) and a variable xi. How can we compute the value of variable xi in the least fixed point of S? The immediate way is to compute bottom-up the least fixed point as described in Equation (11.37), and then look for the value of xi in the least fixed point. But, there is also a query driven method [9]. The method has been used then in [400] as a basis for a query driven ground query answering method for normal logic programs and has further been extended in [289, 413, 414]. This is not surprising, as we have seen in the previous section that the minimal model of K*, i.e., MK, is bijectively related to the least solution of a system of the form (11.36). Hence, if we want to know the truth value of a ground atom A in MK, it suffices to look at the value of the variable xA in the least fixed point of the related equational system.
Initial sets in abstract argumentation frameworks
Published in Journal of Applied Non-Classical Logics, 2018
Recall that the grounded extension of AF is the least fixed point of the characteristic function . Furthermore, it can be built from the initial arguments by collecting the acceptable arguments incrementally. First, we remove the arguments attacked by initial arguments, resulting in a modified argumentation framework. Then, the arguments attacked by the “new” initial arguments can be removed, and so on. This process stops when no new initial argument appears, and all the initial arguments form the grounded extension.
Forecasting with jury-based probabilistic argumentation
Published in Journal of Applied Non-Classical Logics, 2023
Francesca Toni, Antonio Rago, Kristijonas Čyras
The semantics of argumentation can also be characterised by a fixpoint theory of the characteristic function is acceptable with respect to (Dung, 1995). Then S is admissible iff S is conflict-free and . As F is monotonic, it follows that S is a preferred extension iff S is conflict-free and a maximal fixpoint of F. The least fixed point of F gives the grounded extension.
Expressiveness of SETAFs and support-free ADFs under 3-valued semantics
Published in Journal of Applied Non-Classical Logics, 2023
W. Dvořák, A. Keshavarzi Zafarghandi, S. Woltran
Given an ADF , an interpretation v is conflict-free in D iff implies is satisfiable and implies is unsatisfiable;admissible in D iff ;complete in D iff ;grounded in D iff v is the (unique) least fixed-point of ;preferred in D iff v is -maximal admissible in D;a (two-valued) model of D iff v is two-valued and for all , it holds that ;a stable model of D if v is a model of D and , where w is the grounded interpretation of the -reduct , where , , and for each .