Learning Tversky Similarity

In this paper, we advocate Tversky's ratio model as an appropriate basis for computational approaches to semantic similarity, that is, the comparison of objects such as images in a semantically meaningful way. We consider the problem of learning Tversky similarity measures from suitable training data indicating whether two objects tend to be similar or dissimilar. Experimentally, we evaluate our approach to similarity learning on two image datasets, showing that is performs very well compared to existing methods

A Propositional CONEstrip Algorithm

We present a variant of the CONEstrip algorithm for checking whether the origin lies in a finitely generated convex cone that can be open, closed, or neither. This variant is designed to deal efficiently with problems where the rays defining the cone are specified as linear combinations of propositional sentences. The variant differs from the original algorithm in that we apply row generation techniques. The generator problem is WPMaxSAT, an optimization variant of SAT; both can be solved with specialized solvers or integer linear programming techniques. We additionally show how optimization problems over the cone can be solved by using our propositional CONEstrip algorithm as a preprocessor. The algorithm is designed to support consistency and inference computations within the theory of sets of desirable gambles. We also make a link to similar computations in probabilistic logic, conditional probability assessments, and imprecise probability theory

A Lattice Representation of Independence Relations

Independence relations in general include exponentially many statements of independence, that is, exponential in terms of the number of variables involved. These relations are typically fully characterised however, by a small set of such statements and an associated set of derivation rules. While various computational problems on independence relations can be solved by manipulating these smaller sets without the need to explicitly generate the full relation, existing algorithms are still associated with often prohibitively high running times. In this paper, we introduce a lattice representation for sets of independence statements, which provides further insights in the structural properties of independence and thereby renders the algorithms for some well-known problems on independence relations less demanding. By means of experimental results, in fact, we demonstrate a substantial gain in efficiency of closure computation of semi-graphoid independence relations

Task Planning and Partial Order Planning: A Domain Transformation Approach

1 Introduction In the last years many papers have dealt with Hierarchical Task Network (HTN) approach in AI planning ([15],[7],[5],[8],[6]). The success of this approach is due to its effectiveness from both the expressivity and computational sides. The works of Yang [15], Erol et al.[5] [7] and Kambhampati [10] have extensively investigated semantics and complexity of this approach. They show that HTN is strictly more powerful than ordinary (STRIPS-like) planning. This result basically derives from the fact that the set of solution plans of an ordinary planning problem is a regular language, while the set of solution plans of HTN planning problems is a higher level language, (i.e. the solutions space can be expressed as intersection of context free languages)

Closure of independencies under Graphoid properties: some experimental results

In this paper we describe an algorithm for computing the closure with respect to graphoid properties of a set of independencies. Since the computation of the complete closure is infeasible, we provide a procedure, called FC1, which is based on a unique inference rule and on the elimination of redundant independencies. FC1 is able to compute a reduced form of the closure, called fast closure, which is equivalent to the complete closure, but whose size is much smaller. Some experimental tests have been performed with an implementation of the procedure in order to show the computational behavior of the algorithm. We have also compared the computational cost and the size of the fast closure with the corresponding data for the complete closure

A Lattice Representation of Independence Relations

Independence relations in general include exponentially many statements of independence, that is, exponential in terms of the number of variables involved. These relations are typically fully characterised however, by a small set of such statements and an associated set of derivation rules. While various computational problems on independence relations can be solved by manipulating these smaller sets without the need to explicitly generate the full relation, existing algorithms are still associated with often prohibitively high running times. In this paper, we introduce a lattice representation for sets of independence statements, which provides further insights in the structural properties of independence and thereby renders the algorithms for some well-known problems on independence relations less demanding. By means of experimental results, in fact, we demonstrate a substantial gain in efficiency of closure computation of semi-graphoid independence relations