Automated reasoning with function evaluation for COCOLOG

The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, first-order Automated Theorem Proving (ATP) systems - the world championship for such systems. In addition to the primary aim of evaluating the relative capabilities of ATP systems, CASC aims to stimulate ATP research in general, to stimulate ATP research towards autonomous systems, to motivate implementation and fixing of systems, to provide an inspiring environment for personal interaction between ATP researchers, and to expose ATP systems within and beyond the ATP community. Fulfillment of these objectives provides stimulus and insight for the development of more powerful ATP systems, leading to increased and more effective usage. CASC-J4 was held on 13th August 2008, as part of the 4th International Joint Conference on Automated Reasoning, in Sydney, Australia. It was the thirteenth competition in the CASC series (lucky for some). The CASC-J4 web site provides access to details of the competition design, competition resources, and the systems that were entered: http://www.tptp.org/CASC/J4/

Automated theorem provers for first-order logic usually operate on sets of first-order clauses. It is well-known that the translation of a formula in full first-order logic to a clausal normal form (CNF) can crucially affect performance of a theorem prover. In our recent work we introduced a modification of first-order logic extended by the first class boolean sort and syntactical constructs that mirror features of programming languages. We called this logic FOOL. Formulas in FOOL can be translated to ordinary first-order formulas and checked by first-order theorem provers. While this translation is straightforward, it does not result in a CNF that can be efficiently handled by state-of-the-art theorem provers which use superposition calculus. In this paper we present a new CNF translation algorithm for FOOL that is friendly and efficient for superposition-based first-order provers. We implemented the algorithm in the Vampire theorem prover and evaluated it on a large number of problems coming from formalisation of mathematics and program analysis. Our experimental results show an increase of performance of the prover with our CNF translation compared to the naive translation.

We present a theorem prover for possibilistic logic extended with fuzzy constants and fuzzy quantifiers (PLFC), using system KOMET, a general theorem prover system based on generalized annotated logic (GAL). In a previous work (P. Kullman and S. Sandri, 1999), we verified the formal transformation of PLFC with Horn clauses into GAL. The authors discuss some implementation issues and present some examples.

Chapter 9 - Some Proof Procedures Based on Herbrand's Theorem

This paper describes the design and implementation of a control system that integrates visual and haptic information to give assistive force feedback through a haptic controller (Omni Phantom) to the user. A sensor-based assistive function and velocity scaling program provides force feedback that helps the user complete trajectory following exercises for rehabilitation purposes. This system also incorporates a PUMA robot for teleoperation, which implements a camera and a laser range finder, controlled in real time by a PC, were implemented into the system to help the user to define the intended path to the selected target. The real-time force feedback from the remote robot to the haptic controller is made possible by using effective multithreading programming strategies in the control system design and by novel sensor integration. The sensor-based assistant function concept applied to teleoperation as well as shared control enhances the motion range and manipulation capabilities of the users executing rehabilitation exercises such as trajectory following along a sensor-based defined path. The system is modularly designed to allow for integration of different master devices and sensors. Furthermore, because this real-time system is versatile the haptic component can be used separately from the telerobotic component; in other words, one can use the haptic device for rehabilitation purposes for cases in which assistance is needed to perform tasks (e.g., stroke rehab) and also for teleoperation with force feedback and sensor assistance in either supervisory or automatic modes.

At the University of Nevada, Reno, we strongly believe that effective control system education must include experimental exercises that complement the theory presented in lectures. Preferably, the exercises should include the design and implementation of a control system. Limited resources and a cap on the number of credit hours required for the undergraduate degree make it impossible to offer a laboratory course with every control class in most electrical engineering curricula. We have solved this problem by including a laboratory project in each of our two senior electives. Each project is a comprehensive modeling, analysis, design and implementation of a physical control system. The students are divided into groups and each group must independently complete the design project and submit a formal report summarizing their results and experiences. Each student must submit an individual commentary on the exercise and the experimental results obtained. Student feedback indicates an increased appreciation of the lecture material and an awareness of the limitations of the theory and simulation that was lacking prior to the introduction of laboratory exercises.

We propose a combination of model checking and interactive theorem proving where the theorem prover is used to represent finite and infinite state systems, reason about them compositionally and reduce them to small finite systems by verified abstractions. As an example we verify a version of the Alternating Bit Protocol with unbounded lossy and duplicating channels: the channels are abstracted by interactive proof and the resulting finite state system is model checked.KeywordsModel CheckTheorem ProverState ComponentInteractive ProofInteractive TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In recent years there has been a growing demand for Automated Theorem Proving (ATP) in large theories, which often have more axioms than can be handled effectively as normal internal axioms. This work addresses the issues of accessing external sources of axioms from a first-order logic ATP system, and presents an implemented ATP system that retrieves external axioms asynchronously, on demand.

Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, for example, 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 i>positive unit hyperresolution (i>PUHR) i>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 i>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.

Conditional and Preferential Logics: Proof Methods and Theorem Proving

Implementation of automatic heating control systems will reduce heat consumption by 10% in administrative and 40% in educational buildings. The most effect of supply of comfortable microclimate with minimum energy consumption is achieved by using dynamic multi-zone control of each room heating in abuilding according to changing of external and internal exposure and usage schedule of that room. However, implementation of that control system is affected by the issue of unbalanced heating flows. That’s why it is necessary to develop an imitation model of heat flows redistribution for synthesizing the system of interconnected dynamic heating control in a building, including coolant heating flow control.

This paper aims to discuss the design and implementation of automatic control system for chemical production line based on PLC. With the rapid development of chemical industry and the intensification of market competition, it has become an important demand for chemical enterprises to improve production efficiency, ensure product quality and realize automation and intelligence of production process. Firstly, this paper analyzes the characteristics and requirements of chemical production line, as well as the requirements and objectives of automatic control system. Then, the overall architecture design, hardware design, software design, system implementation and testing process of the automatic control system of chemical production line based on PLC are described in detail. The feasibility and effectiveness of the system are verified by the analysis of practical application cases. The research results show that the automatic control system of chemical production line based on PLC can significantly improve production efficiency, reduce production costs, ensure product quality and enhance the market competitiveness of chemical enterprises. The research in this paper provides new ideas and methods for the design and implementation of automatic control system in chemical industry.

Research on features has received much attention in the domain engineering community. Feature modeling plays an important role in the design and implementation of complex software systems. However, the presentation and analysis of feature models are still largely informal. There is also an increasing need for methods and tools that can support automated feature model analysis. This paper presents a formal engineering approach to the specification and verification of feature models. A formal semantics for the feature modeling language is defined using first-order logic. It provides a precise and rigorous formal interpretation for the graphical notation. In addition, further validation of the semantics using the Z/EVES theorem prover is presented. Finally, we demonstrate that the consistency of a feature model and its configurations can be automatically verified by encoding the semantics into the Alloy Analyzer. A case study of the Key Word in Context (KWIC) index systems feature model is presented to illustrate the verification process.

Preface: Volume 59, Issue 4

This paper presents an improvement of Herbrand's theorem. We propose a method for specifying a subuniverse of the Herbrand universe of a clause set S for each argument of predicate symbols and function symbols in S. We prove that a clause set S is unsatisfiable if and only if there is a finite unsatisfiable set of ground instances of clauses of S that are derived by only instantiating each variable, which appears as an argument of predicate symbols or function symbols, in S over its corresponding argument's sub-universe of the Herbrand universe of S. Because such sub-universes are usually smaller (sometimes considerably) than the Herbrand universe of S, the number of ground instances may decrease considerably in many cases. We present an algorithm for automatically deriving the sub-universes for arguments in a given clause set, and show the correctness of our improvement. Moreover, we introduce an application of our approach to model generation theorem proving for non-range-restricted problems, show the range-restriction transformation algorithm based on our improvement and provide examples on benchmark problems to demonstrate the power of our approach.