The paper deals with the valued comparison of intervals for decision making. Interval orders are classical preference structures where the comparison of intervals is done in an ordinal way. In this paper we focus on valued comparison where more information, especially the distance between end-points of intervals, is used in order to have more sophisticated preference relations. The generalizati...

The non-monotone dualization (NMD) is one of the most essential tasks required for finding hypotheses in various ILP settings, like learning from entailment [1, 2] and learning from interpretations [3]. Its task is to generate an irredundant prime CNF formula ψ of the dual f where f is a general Boolean function represented by CNF [4]. The DNF formula φ of f is easily obtained by De Morgan’s la...

Given a lattice (X,≤,∧,∨) we define a multi-valued operation ∧ which is analogous to a t-norm (i.e. it is commutative, associative, has one as a neutral element and is monotone). The operation is parametrized by the set Q, hence we actually obtain an entire family of such multi-valued t-norms. Similarly we define a family of multi-valued t-conorms ∨ . We show that, when P, Q are chosen appropri...

In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to re...

This paper takes part in the discussion motivated by Elkan's paper ``The Paradoxical Success of Fuzzy Logic'' printed in 1993, whose main theoretical point was that Fuzzy Logic does not properly deal with a speci®c Law of Classical Logic: :…p ^ :q† ˆ q _ …:p ^ :q†. The given answer can be summarized, like in other previous cases, by the sentence ``Yes it can but, of course, at some cost''. As i...

1 Ward, Morgan, "Memoir on Elliptic Divisibility Sequences," Am. J. Math., 70, 31-74 (1948). 2 Ward, Morgan, "Arithmetical Properties of Polynomials Associated with the Lemniscate Elliptic Functions," PROC. NATL. ACAD. Sci., 36, 359-362 (1950). 3 For the three-term sigma formula, and all of the formulas of the previous paragraph, cf. Tannery and Molk, Pl1ments de la theorie des fonctions ellipt...

The term “eponym” originates from the Greek word “eponymous”, which means “named after”. Dermatology literature is rich in eponyms [1]. In this communication, we aimed to highlight on selected eponyms in dermatology literature linked to the vascular tumors, which we listed it in in Table I [1-7]. However, we want to stress that this table is by no mean conclusive as some eponyms linked to vascu...

Refine is a tool that supports the application of Morgan’s refinement calculus. It was designed to support teaching and use by beginners; it is already in use. We describe here the extension of Refine to support the development of (possibly recursive) procedures in the algebraic style of the refinement calculus already adopted by Refine. Resumo. Refine é uma ferramenta que suporta a aplicação d...

In 1860, Augustus de Morgan published DeM60], thereby launching an investigation into the algebra of relations. This developed into the subject now called Algebraic Logic, though in the 19th century it was simply thought of as mathematical logic. This work, along with Frege's quantiier logic, became the foundation of modern logic and model theory. In De Morgan's writing there is no sharp separa...

Translational Cancer Research Unit Antwerp, Oncology Center, General Hospital Sint-Augustinus, Wilrijk, Belgium 2 Department Oncology, KU Leuven, Leuven, Belgium 3 Morgan Welch Inflammatory Breast Cancer Program and Clinic, The University of Texas MD Anderson Cancer Center, Houston, TX, USA Département d'Oncologie Moléculaire, Centre de Recherche en Cancérologie de Marseille, UMR891 Inserm, Ins...