This work describes a methodology to combine logic-based systems and connectionist systems. Our approach uses finite truth valued Lukasiewicz logic, where we take advantage of fact, presented by Castro in [6], what in this type of logics every connective can be define by a neuron in an artificial network having by activation function the identity truncated to zero and one. This allowed the inje...

In this paper, we proposed an image inpainting algorithm, including interpolation step and a non-local tensor completion based on weighted nuclear norm. Specifically, the algorithm adopts triangular linear firstly to preform observation image. Second, extract similar patches in using patch match rearrange them tensor. Then, use norm recover tensors. Finally, regroup all these recovered tensors ...

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Lukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all insta...

The paper continues the study of recently introduced class SDD1 matrices. general matrices and its three subclasses are considered. In particular, it is shown that nonsingular ℌ-matrices. Also parameter-free upper bounds for l∞-norm inverses to derived. block triangular form which any matrix can be brought by a symmetric permutation rows columns described.

Keywords: mathematical fuzzy logic, basic fuzzy logic, monoidal t-norm logic, hoop logic, non-commutative fuzzy logic. This paper is a companion to my [12]. The latter is a rather technical paper developing a generalized (mathematical) fuzzy logic. Main definitions and results of [12] are reproduced here without any proofs; but this is preceded by a survey on the basic proposi-tional fuzzy logi...

In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this...

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages ...