Space Efficiency of Propositional Knowledge Representation Formalisms

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class

Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation

Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of first-order clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depth-first relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MM-SATCHMO, of this procedure is given and its performance on benchmark suites is reported. The second minimal model generation procedure performs a breadth-first, constrained expansion of PUHR (complement) tableaux. Both procedures are optimal in the sense that each minimal model is constructed only once, and the construction of nonminimal models is interrupted as soon as possible. They are complete in the following sense The depth-first minimal model generation procedure computes all minimal Herbrand models of the considered clauses provided these models are all finite. The breadth-first minimal model generation procedure computes all finite minimal Herbrand models of the set of clauses under consideration. The proposed procedures are compared with related work in terms of both principles and performance on benchmark problems

The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Theory, Implementation and Experiments

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state of the art abductive systems and answer set solvers and showing how to use it to program some applications. (To appear in Theory and Practice of Logic Programming - TPLP)

Hybrid ASP-based Approach to Pattern Mining

Detecting small sets of relevant patterns from a given dataset is a central challenge in data mining. The relevance of a pattern is based on user-provided criteria; typically, all patterns that satisfy certain criteria are considered relevant. Rule-based languages like Answer Set Programming (ASP) seem well-suited for specifying such criteria in a form of constraints. Although progress has been made, on the one hand, on solving individual mining problems and, on the other hand, developing generic mining systems, the existing methods either focus on scalability or on generality. In this paper we make steps towards combining local (frequency, size, cost) and global (various condensed representations like maximal, closed, skyline) constraints in a generic and efficient way. We present a hybrid approach for itemset, sequence and graph mining which exploits dedicated highly optimized mining systems to detect frequent patterns and then filters the results using declarative ASP. To further demonstrate the generic nature of our hybrid framework we apply it to a problem of approximately tiling a database. Experiments on real-world datasets show the effectiveness of the proposed method and computational gains for itemset, sequence and graph mining, as well as approximate tiling. Under consideration in Theory and Practice of Logic Programming (TPLP).Comment: 29 pages, 7 figures, 5 table