Fuzzy Maximum Satisfiability

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.Comment: 10 page

The Political Basis of Abstraction in the 20th Century as Explored by a Painter

The political nature of abstraction presented from an artist’s point of view – one who considers the most advanced task is the exploration of the language of pictures. Such exploration is understood as a separate discipline from the many others that employ pictures for practical functions. The author examines the development of 20th century abstraction as an effect of revolutionary social motion. Historic steps to abstraction, taking shape as rising and receding artistic movements, are correlated to revolutionary motion. The materialist underpinning of abstraction is distinguished from the idealism of Post-Modernism. The paper ends with an examination of contemporary discourse in the Western art world that attempts to erase the internationalism of abstraction and, thereby, marginalize non-Western practitioners