Ulrich Furbach

Computational Logic — CL 2000

Syntax for Variable Binders: An Overview . . . . . . . . . . . . . . . . . . . . 239 Dale Miller Goal-Directed Proof Search in Multiple-Conclusioned Intuitionistic Logic . . 254 James Harland, Tatjana Lutovac, and Michael Winikoff Efficient EM Learning with Tabulation for Parameterized Logic Programs . 269 Yoshitaka Kameya and Taisuke Sato Model Generation Theorem Proving with Finite Interval Constraints . . . . . 285 Reiner Hähnle, Ryuzo Hasegawa, and Yasuyuki Shirai Combining Mobile Processes and Declarative Programming . . . . . . . . . . . . . 300 Rachid Echahed and Wendelin Serwe

Hyper Tableaux with Equality

In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn (only) from a set of positive unit clauses, the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition theorem proving. Our main results are soundness and completeness, but we briefly describe the implementation, too.

An application of automated reasoning in natural language question answering

The LogAnswer system is an application of automated reasoning to the field of open domain question answering. In order to find answers to natural language questions regarding arbitrary topics, the system integrates an automated theorem prover in a framework of natural language processing tools. The latter serve to construct an extensive knowledge base automatically from given textual sources, while the automated theorem prover makes it possible to derive answers by deductive reasoning. In the paper, we discuss the requirements to the prover that arise in this application, especially concerning efficiency and robustness. The proposed solution rests on incremental reasoning, relaxation of the query (if no proof of the full query is found), and other techniques. In order to improve the robustness of the approach to gaps of the background knowledge, the results of deductive processing are combined with shallow linguistic features by machine learning.

Automated Deduction Techniques for the Management of Personalized Documents

This work is about a “real-world” application of automated deduction. The application is the management of documents (such as mathematical textbooks) as they occur in a readily available tool. In this “Slicing Information Technology tool”, documents are decomposed (“sliced”) into small units. A particular application task is to assemble a new document from such units in a selective way, based on the users current interest and knowledge. It is argued that this task can be naturally expressed through logic, and that automated deduction technology can be exploited for solving it. More precisely, we rely on first-order clausal logic with some default negation principle, and we propose a model computation theorem prover as a suitable deduction mechanism. Beyond solving the task at hand as such, with this work we contribute to the quest for arguments in favor of automated deduction techniques in the “real world”. Also, we argue why we think that automated deduction techniques are the best choice here.

A Confluent Connection Calculus

This work is concerned with basic issues of the design of calculi and proof procedures for first-order connection methods and tableaux calculi. Proof procedures for these type of calculi developed so far suffer from not exploiting proof confluence, and very often unnecessarily rely on a heavily backtrack oriented control regime. As a new result, we present a variant of a connection calculus and prove its strong completeness. This enables the design of backtrack-free control regimes. To demonstrate that the underlying fairness condition is reasonably implementable we define an effective search strategy.

Hybrid multiagent systems with timed synchronization: specification and model checking

This paper shows how multiagent systems can be modeled by a combination of UML statecharts and hybrid automata. This allows formal system specification on different levels of abstraction on the one hand and expressing real-time system behavior with continuous variables on the other hand. It is shown, how multi-robot systems can be modeled by hybrid and hierarchical state machines and how model checking techniques for hybrid automata can be applied. An enhanced synchronization concept is introduced that allows synchronization taking time and avoids state explosion to a certain extent.

Formal specification methods for reactive systems

Abstract A tutorial-like overview on formal methods for the specification of reactive systems is given. State transition systems such as ATNs, statecharts, and SDL are discussed. Petri nets and logic-based languages are introduced as alternatives; examples show their respective applicability. Programming-oriented approaches such as ESTEREL, CSP, or CCS are depicted. Finally, the different principles are compared.

Applications of automated reasoning

This paper offers an informal overview and discussion on first order predicate logic reasoning systems together with a description of applications which are carried out in the Artificial Intelligence Research Group of the University in Koblenz. Furthermore the technique of knowledge compilation is shortly introduced.

Model Based Deduction for Database Schema Reasoning

We aim to demonstrate that automated deduction techniques, in particular those following the model computation paradigm, are very well suited for database schema/query reasoning. Specifically, we present an approach to compute completed paths for database or XPath queries. The database schema and a query are transformed to disjunctive logic programs with default negation, using a description logic as an intermediate language. Our underlying deduction system, KRHyper, then detects if a query is satisfiable or not. In case of a satisfiable query, all completed paths – those that fulfill all given constraints – are returned as part of the computed models.

Logic-Based Question Answering

Question answering systems aim to provide concise and correct responses to arbitrary questions, communicating with the user in a natural language. This way they help making the knowledge of large textual sources accessible in an intuitive manner which goes beyond the capabilities of conventional search engines. In the LogAnswer project the universities of Hagen and Koblenz cooperate to build a German language question answering system which combines computational linguistics and automated reasoning to deduce answers from a knowledge base derived from Wikipedia.