Redundancy checking is an important task in AI subfields such as knowledge representation and constraint solving. This paper considers redundant topological constraints, defined in the region connection calculus RCC8. We say a constraint in a set Γ of RCC8 constraints is redundant if it is entailed by the rest of Γ. A prime subnetwork of Γ is a subset of Γ which contains no redundant constraint...

In [14] we showed that for each locally finite unary (total) algebra of finite type, its weak subalgebra lattice uniquely determines its (strong) subalgebra lattice. Now we generalize this fact to algebras having also finitely many binary operations (for example, groupoids, semigroups, semilattices). More precisely, we generalize some ideas from [14] to prove: Let A be a locally finite (total) ...

Corresponding Author: Andréia Alves dos Santos Schwaab Department of Informatics and Statistics, Federal University of Santa Catarina, Florianopolis, Brazil Email:[email protected] Abstract: Generation of membership functions is an important step in construction of fuzzy systems. Since membership functions reflect what is known about the variables involved in a problem, when they are c...

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi [K.G. Murty and S.N. Kabadi, Some NP-complete problems in quadratic and nonlinear programming, Mathematical Programming, 39, no.2:117–129, 1987] that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix...

It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore the existence of such algebras is undecidable in ZFC. In ”forcing language” condition (a) says that there exists a non– trivial σ–centered for...