Subsumption Algorithms for Three-Valued Geometric Resolution

In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains only atoms with variables, equality, and existential quantifiers. The interpretation contains only atoms with constants. Because the atoms have no term structure, matching for geometric resolution is hard. We translate the matching problem into a generalized constraint satisfaction problem, and discuss several approaches for solving it efficiently, one direct algorithm and two translations to propositional SAT. After that, we study filtering techniques based on local consistency checking. Such filtering techniques can a priori refute a large percentage of generalized constraint satisfaction problems. Finally, we adapt the matching algorithms in such a way that they find solutions that use a minimal subset of the interpretation. The adaptation can be combined with every matching algorithm. The techniques presented in this paper may have applications in constraint solving independent of geometric resolution.Comment: This version was revised on 18.05.201

Simplification of many-valued logic formulas using anti-links

We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called "removal of anti-links". Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formula themselves, rather, they remove certain forms of redundancy from formulas in negation normal form (NNF). Their main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we define an anti-link operation on a generic language for expressing many-valued logic formulas called "signed NNF" and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way

Introduction: Legal Form and Cultural Symbol – Music, Copyright and Information Studies

Writers in information and communication studies often assume the stability of objects under investigation: network nodes, databases, information. Legal writers in the intellectual property tradition often assume that cultural artefacts exist as objects prior to being governed by copyright law. Both assumptions are fallacious. This introduction conceptualises the relationship of legal form and cultural symbol. Starting from an understanding of copyright law as part of systems of production (in the sense of Peterson 1976), it is argued that copyright law constructs the artefacts it seeks to regulate as objects that can be bought and sold. In doing so, the legal and aesthetic logic of cultural symbols may clash, as in the case of digital music (the central focus of this special issue)

Hypergraph Acyclicity and Propositional Model Counting

We show that the propositional model counting problem #SAT for CNF- formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore, we present a polynomial time algorithm that computes a disjoint branches decomposition of a given hypergraph if it exists and rejects otherwise. Finally, we show that some slight extensions of the class of hypergraphs with disjoint branches decompositions lead to intractable #SAT, leaving open how to generalize the counting result of this paper

Fuzzy weakest precondition and fuzzy invariants

Design and formal verification of algorithms can be translated into a fuzzy framework introducing fuzzy logic and assert transformations. Following the classical scheme, and in order to develop codes with good behavior, this paper defines the concepts of fuzzy algorithm specification and fuzzy weakest precondition operator which are then applied to a fuzzy decision making algorithm. Keywords: Fuzzy algorithms and programming,decision making