Jieh Hsiang

Refutational theorem proving using term-rewriting systems

Abstract In this paper we propose a new approach to theorem proving in first-order logic based on the term-rewriting method. First for propositional calculus, we introduce a canonical term-rewriting system for Boolean algebra. This system enables us to transform the first-order predicate calculus into a form of equational logic, and to develop several complete strategies (both clausal and nonclausal) for first-order theories based on the Knuth-Bendix Completion Procedure. More importantly, our strategies can deal with predicate logic and built-in (equational) theories in a uniform and effective way. We also describe an implementation and comparisons with some other first-order theorem-proving methods.

PSATO: a distributed propositional prover and its application to quasigroup problems

Abstract We present a distributed/parallel prover for propositional satisfiability (SAT), called PSATO, for networks of workstations. PSATO is based on the sequential SAT prover SATO, which is an efficient implementation of the Davis –Putnam algorithm. The master–slave model is used for communication. A simple and effective workload balancing method distributes the workload among workstations. A key property of our method is that the concurrent processes explore disjoint portions of the search space. In this way, we use parallelism without introducing redundant search. Our approach provides solutions to the problems of (i) cumulating intermediate results of separate runs of reasoning programs; (ii) designing highly scalable parallel algorithms and (iii) supporting “fault-tolerant” distributed computing. Several dozens of open problems in the study of quasigroups have been solved using PSATO. We also show how a useful technique called the cyclic group construction has been coded in propositional logic.

On word problems in equational theories

The Knuth-Bendix procedure for word problems in universal algebra is known to be very effective when it is applicable. However, the procedure will fail if it generates equations which cannot be oriented into rules (i.e., the system is not noetherian), or if it generates infinitely many rules (i.e., the system is not confluent). In 1981 Huet showed that even if the system is not confluent, the Knuth-Bendix procedure still yields a semi-decision procedure for word problems, provided that every equation can be oriented. In this paper we show that even if some equations are not orientable, the Knuth-Bendix procedure can still be modified into a reasonably efficient semi-decision procedure for word problems in equational theories. Thus, we have lifted the noetherian requirement in the Knuth-Bendix procedure. Several confluence results, extensions, and experiments are given. So are some comparisons with related work.

Proving refutational completeness of theorem-proving strategies: the transfinite semantic tree method

In this paper, a proof method based on a notion of transfinite semantic trees is presented and it is shown how to apply it to prove the completeness of refutational theorem proving methods for first order predicate calculus with equality. To demonstrate how this method is used, the completeness of two theorem-proving strategies, both refinements of resolution and paramodulation, are proved. Neither of the strategies need the functionally reflexive axioms nor paramodulating into variables. Therefore the Wos-Robinson conjecture follows as a corollary. Another strategy for Horn logic with equality is also presented.

Rewrite Methods for Clausal and Non-Clausal Theorem Proving

Effective theorem provers are essential for automatic verification and generation of programs. The conventional resolution strategies, albeit complete, are inefficient. On the other hand, special purpose methods, such as term rewriting systems for solving word problems, are relatively efficient but applicable to only limited classes of problems.

Various criteria in the evaluation of biomedical named entity recognition

BackgroundText mining in the biomedical domain is receiving increasing attention. A key component of this process is named entity recognition (NER). Generally speaking, two annotated corpora, GENIA and GENETAG, are most frequently used for training and testing biomedical named entity recognition (Bio-NER) systems. JNLPBA and BioCreAtIvE are two major Bio-NER tasks using these corpora. Both tasks take different approaches to corpus annotation and use different matching criteria to evaluate system performance. This paper details these differences and describes alternative criteria. We then examine the impact of different criteria and annotation schemes on system performance by retesting systems participated in the above two tasks.ResultsTo analyze the difference between JNLPBAs and BioCreAtIvEs evaluation, we conduct Experiment 1 to evaluate the top four JNLPBA systems using BioCreAtIvEs classification scheme. We then compare them with the top four BioCreAtIvE systems. Among them, three systems participated in both tasks, and each has an F-score lower on JNLPBA than on BioCreAtIvE. In Experiment 2, we apply hypothesis testing and correlation coefficient to find alternatives to BioCreAtIvEs evaluation scheme. It shows that right-match and left-match criteria have no significant difference with BioCreAtIvE. In Experiment 3, we propose a customized relaxed-match criterion that uses right match and merges JNLPBAs five NE classes into two, which achieves an F-score of 81.5%. In Experiment 4, we evaluate a range of five matching criteria from loose to strict on the top JNLPBA system and examine the percentage of false negatives. Our experiment gives the relative change in precision, recall and F-score as matching criteria are relaxed.ConclusionIn many applications, biomedical NEs could have several acceptable tags, which might just differ in their left or right boundaries. However, most corpora annotate only one of them. In our experiment, we found that right match and left match can be appropriate alternatives to JNLPBA and BioCreAtIvEs matching criteria. In addition, our relaxed-match criterion demonstrates that users can define their own relaxed criteria that correspond more realistically to their application requirements.

An architecture and category knowledge for intelligent information retrieval agents

Abstract Information overload has become a serious problem for users of the World Wide Web. In this paper, we propose to use intelligent information retrieval (IIR) agents as a solution to this problem. We identify desirable features of an IIR agent, including intelligent search, navigation guide, auto-notification, personal information management, dynamic personalized Web pages, and tools for page reading-aide. We propose a modularized agent architecture, describe the responsibility of each component and discuss how to combine these components to perform various tasks. We point out that group knowledge, acquired from preferences of other users in the same group, may be useful. The agents knowledge on user preference is primarily represented by category profiles. Several applications of category profiles are also investigated.

A new method for establishing refutational completeness in theorem proving

We present here a new technique for establishing completeness of refutational theorem proving strategies. This method employs semantic trees and, in contrast to most of the semantic tree methods, is based on proof by refutation instead of proof by induction. Thus, it works well on transfinite semantic trees as well as on finite ones. This method is particularly useful for proving the completeness of strategies with the presence of the equality predicate. We have used the method to prove the completeness of the following strategies (without the need of the functional reflexive axioms), where the precise definition of oriented paramodulation will be given later.

Integrating linguistic knowledge into a conditional random fieldframework to identify biomedical named entities

As new high-throughput technologies have created an explosion of biomedical literature, there arises a pressing need for automatic information extraction from the literature bank. To this end, biomedical named entity recognition (NER) from natural language text is indispensable. Current NER approaches include: dictionary based, rule based, or machine learning based. Since, there is no consolidated nomenclature for most biomedical NEs, any NER system relying on limited dictionaries or rules does not seem to perform satisfactorily. In this paper, we consider a machine learning model, CRF, for the construction of our NER framework. CRF is a well-known model for solving other sequence tagging problems. In our framework, we do our best to utilize available resources including dictionaries, web corpora, and lexical analyzers, and represent them as linguistic features in the CRF model. In the experiment on the JNLPBA 2004 data, with minimal post-processing, our system achieves an F-score of 70.2%, which is better than most state-of-the-art systems. On the GENIA 3.02 corpus, our system achieves an F-score of 78.4% for protein names, which is 2.8% higher than the next-best system. In addition, we also examine the usefulness of each feature in our CRF model. Our experience could be valuable to other researchers working on machine learning based NER.

Automated proofs of the Moufang identities in alternatives rings

In this paper we present automatic proofs of the Moufang identities in alternative rings. Our approach is based on the term rewriting (Knuth-Bendix completion) method, enforced with various features. Our proofs seem to be the first computer proofs of these problems done by a general purpose theorem prover. We also present a direct proof of a certain property of alternative rings without employing any auxiliary functions. To our knowledge our computer proof seems to be the first direct proof of this property, by human or by a computer.