Miyuki Koshimura

Embedding Negation as Failure into a Model Generation Theorem Prover

Here, for the first time, we give an implementation which computes answer sets of every class of (function-free) logic programs and deductive databases containing both negation as failure and classical negation. The proposal is based on bottom-up, incremental, backtrack-free computation of the minimal models of positive disjunctive programs, together with integrity constraints over beliefs and disbeliefs. Our translation method not only provides a simple fixpoint characterization of answer sets, but also is very helpful to understand under what conditions each model is “stable” or “unstable”. The procedure has been implemented on top of the model generation theorem prover MGTP on a parallel inference machine, and has been applied to a legal reasoning system.

Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving

We present a new method, called non-Horn magic sets (NHM), to enhance forward reasoning provers by combining top-down and bottom-up computations. This method is a natural extension of Horn magic sets and is applicable to range-restricted non-Horn clauses. We show two types of transformations to get non-Horn magic sets from the given clause sets: breadth-first NHM and depth-first NHM. The first transformation evaluates the antecedent atoms of an original clause in parallel. The second one evaluates them sequentially while propagating the bindings in an antecedent atom to the next by using continuation predicates. These transformations are shown to be sound and complete. The NHM method has been implemented on a UNIX workstation. We evaluated effects of NHM by proving some typical problems taken from the TPTP problem library.

MGTP: A Parallel Theorem Prover Based on Lazy Model Generation

We have implemented a model-generation based parallel theorem prover in KL1 on a parallel inference machine, PIM. We have developed several techniques to improve the efficiency of forward reasoning theorem provers based on lazy model generation. The tasks of the model-generation based prover are the generation and testing of atoms to be the elements of a model for the given theorem. The problem with this method is the explosion in the number of generated atoms and in the computational cost in time and space, incurred by the generation processes. Lazy model generation is a new method that avoids the generation of unnecessary atoms that are irrelevant to obtaining proofs, and to provide flexible control for the efficient use of resources in a parallel environment. With this method we have achieved a more than one-hundred-fold speedup on a PIM consisting of 128 PEs.

Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers

Totalizer (TO) by Bailleux et al. and Half Sorting Network (HS) by Asin et al. are typical CNF encoding methods of cardinality constraint. The former is based on unary adder, while the latter is based on odd-even merge. Although TO is inferior to HS in terms of the number of clauses, TO is superior to HS in terms of the number of variables. We propose a new method called Modulo Totalizer (MTO) to overcome the disadvantage of TO. As an application, we have developed a partial MaxSAT solver with MTO. Preliminary experimental results show that our MTO based MaxSAT solver is comparable to or surpass the conventional TO based maxsat solvers.

Efficient Minimal Model Generation Using Branching Lemmas

An efficient method for minimal model generation is presented. The method employs branching assumptions and lemmas so as to prune branches that lead to nonminimal models, and to reduce minimality tests on obtained models. This method is applicable to other approaches such as Bry’s complement splitting and constrained search or Niemela’s groundedness test, and greatly improves their efficiency. We implemented MM-MGTP based on the method. Experimental results with MM-MGTP show a remarkable speedup compared to MM-SATCHMO.

MGTP: A Model Generation Theorem Prover - Its Advanced Features and Applications

This paper outlines a parallel model-generation based theorem-proving system MGTP that we have been developing, focusing on the recent developments including novel techniques for efficient proof-search and successful applications.

Solving the Coalition Structure Generation Problem with MaxSAT

Coalition Structure Generation (CSG), a main research issue in the domain of coalition games, involves partitioning agents into exhaustive and disjoint coalitions so that the social welfare is optimized. The advent of compact representation schemes, such as marginal contribution networks (MC-nets), promotes the efficiency of solving the CSG problem. In this paper, inspired by the dramatic speed-up of Boolean Satisfiability Problem (SAT) solvers, we make the first step towards a study of applying MaxSAT solvers to the CSG problem. We set out to encode the MC-nets into propositional Boolean logic and utilize an off-the-shelf MaxSAT solver as an optimization tool for solving the CSG problem. Specifically, based on the previous works, we encode rule relations and their constraints into weighted partial MaxSAT formulas and show that MaxSAT solvers are useful in solving the CSG problem. Furthermore, we put forward a brand-new method based on agent relations which specify whether two agents of a rule are in the same coalition. Experimental evaluations show that our methods outperform other state-of-the-art algorithms.

Proof simplification for model generation and its applications

Proof simplification eliminates unnecessary parts from a proof leaving only essential parts in a simplified proof. This paper gives a proof simplification procedure for model generation theorem proving and its applications to proof condensation, folding-up and completeness proofs for non-Horn magic sets. These indicate that proof simplification plays a useful role in theorem proving.

Personalized Search Using ODP-based User Profiles Created from User Bookmark

When searching for intended pages on the Internet, users often have a hard time to find the pages because the pages do not always come at the higher rank of searched results. The Personalized Search is a promising approach to solve this problem. In the Personalized Search, User Profiles (UPs in short) that represent interests of the users, are well used and often created from personal documents of the users. This paper proposes (1) a method for making UPs based on Open Directory Project (ODP) and shows (2) a Personalized Search system using the UPs made from Book Marks. Some of experimental results illustrate the validity of our method for making the UPs, and show the precision enhancement of this system.

Quality Improvement of Clustering Engine in the Internet Based on Correlation

Search engines give so many results that a user cannot handle them all in a short period of time. Many approaches have been proposed to alleviate this problem. For example, some approaches try to add personalized features and some try to group the results into different categories. The latter one is called a clustering engine, which is the emphasis of this paper. It first reviews several existing approaches such as STC, SHOC, LINGO and SnakeT. It then gives a new approach called HICSEC (Hierarchical Clustering Search Engine with Correlation) to improve the accuracy of clustering by the Correlation calculated with the Singular Value Decomposition.