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An intelligent modeling and analysis method of manufacturing process using the first-order predicate logic

COMPUTERS & INDUSTRIAL ENGINEERING 2009年第4期56卷 1559-1565页

作者： Wang Zhenwei Du Pingan Yu Yating Univ Elect Sci & Technol China Inst Aeronaut & Astronaut Chengdu 610054 Peoples R China Univ Elect Sci & Technol China Sch Mechatron Engn Chengdu 610054 Peoples R China

Manufacturing process refers to machining sequence from raw materials to final products. Process plan has important effects on manufacturing process. In general, process designer relies on his experience and knowledge to arrange the process plan. For a complex part, it takes long time and effort to determine process plan. In this paper, an intelligent modeling and analysis method using the first-order predicate logic is proposed to evaluate the manufacturing performance. first, the logic predicates used to represent the process plan are defined according to the machining methods, and the predicate variables are discussed in detail. Consequently, the process plan can be represented in the form of the first-order predicate logic. Second, a type of element model composed of four nodes and four links is put forward in order to construct the process model. All components in this element model are respectively explained, and the mapping relationship between element model and predicate logic is described in detail. According to engineering practices, logic inference rules are suggested and the inference process is illustrated. Hence, the manufacturing process model can be constructed. Third, the process simulation is carried out to evaluate the performance of manufacturing system by using measures such as efficiency, the machine utilization, etc. Finally, a case study is given to explain this intelligent modeling method using the first-order predicate logic. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Manufacturing process Intelligent modeling first-order predicate logic Process simulation

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Binary decision diagrams for first-order predicate logic

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JOURNAL OF logic AND ALGEBRAIC PROGRAMMING 2003年第1-2期57卷 1-22页

作者： Groote, JF Tveretina, O Eindhoven Univ Technol Dept Comp Sci Sect Tech NL-5600 MB Eindhoven Netherlands

Binary decision diagrams (BDDs) are known to be a very efficient technique to handle propositional formulas. We present an extension of BDDs such that they can be used for predicate logic. We define BDDs similar to Bryant [IEEE Trans. Comp. C-35 (1986) 677-691], but with the difference that we allow predicates as labels instead of proposition symbols. We present a sound and complete proof search method for first-order predicate logic based on BDDs which we apply to a number of examples. (C) 2003 Elsevier Inc. All rights reserved.

关键词： automatic reasoning binary decision diagrams first-order predicate logic

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Formal modelling of a sheet metal smart manufacturing system by using Petri nets and first-order predicate logic

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JOURNAL OF INTELLIGENT MANUFACTURING 2021年第4期32卷 1043-1063页

作者： Lu, Juan Ou, Chengyi Liao, Chen Zhang, Zhenkun Chen, Kai Liao, Xiaoping Guangxi Univ Guangxi Key Lab Mfg Syst & Adv Mfg Technol Nanning 530004 Peoples R China Beibu Gulf Univ Dept Mech & Marine Engn Qinzhou 535011 Peoples R China Guangxi Univ Dept Mech Engn Nanning 530004 Peoples R China Guangxi Automobile Grp Co Ltd Liuzhou Peoples R China Shenzhen Cyberspace Lab Pengcheng Lab Shenzhen 518055 Peoples R China

This study introduces a developed method to a smart computer-aided design/manufacturing (CAD/CAM) system, where layout design, process planning, and comprehensive computerized numerical control (CNC) code generation can be implemented to satisfy laser cutting holes, tapping, irregular and complicated profile processing, engraving, and burr back-scraping. The smart CAD/CAM(SCAM) system is developed as a commercial software product or application and firstly applied to flexible sheet metal machining center (BGL 130R). In this study, a formal modeling method involving Petri nets and first-order predicate logic is proposed to develop the smart manufacturing system. High-level Petri nets are employed to achieve the formal application architecture design of data flow for various functions, and the first-order logic used to represent the process plan is defined and deduced according to the machining methods. The developed system possesses the following characteristics: (1) a sound and complete deductive system to implement various types of trajectory planning, automatic generation, and validation of the CNC code;(2) a convenient design input environment and readiness for re-design and modification by adding specific design functions and using standard design procedures on a widely used CAD/CAM package;(3) helpful for designers in sheet metal layout designing, layout interference detection, process planning validation, preprocess manufacturing operation of CNC code generation, and autodefinition of storable file names;and (4) formal and simple in human-computer interaction, automatic and intelligent in process operations, and satisfactory in terms of the requirements of the flexible sheet metal machining center (BGL 130R).

关键词： Smart CAD CAM High-level petri nets Object-oriented programming first-order predicate logic Process planning Layout design

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Semantical Completeness of first-order predicate logic and the Weak Fan Theorem

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STUDIA logicA 2015年第3期103卷 623-638页

作者： Krivtsov, Victor N. Moscow MV Lomonosov State Univ Fac Mech & Math Dept Math Log & Theory Algorithms Moscow 127051 Russia Moscow State Univ Psychol & Educ Fac Appl Math Moscow 127051 Russia

Within a weak system of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over the Weak Fan Theorem.

关键词： first-order predicate logic Semantical completeness The Weak Fan Theorem

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Heterogeneous-branch integration framework: Introducing first-order predicate logic in logical Reasoning Question Answering

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NEUROCOMPUTING 2024年 609卷

作者： Yue, Jianyu Bi, Xiaojun Chen, Zheng Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Peoples R China Minzu Univ China Key Lab Ethn Language Intelligent Anal & Secur Gov Beijing 100081 Peoples R China Minzu Univ China Sch Informat & Engn Beijing 100081 Peoples R China

The logical reasoning question-answering is a critical task in natural language processing, as it equips models with human-like logical reasoning intelligence. Existing approaches focus on extracting and leveraging the hidden logical structures within text. However, previous works explore partial logical relationships and neglect the holistic extraction within the text. Moreover, they struggle to fully model logical connections, including long-distance dependencies and local topology information. To address these issues, we propose a novel heterogeneous-branch integration framework. Our framework is based on first-order predicate logic theory and consists of three primary components. first, we construct two heterogeneous logical graphs to model logical relationships within and between propositions. Second, we propose a novel Graph-Masked Transformer with a novel graph-masked multi-head attention mechanism to enable distant node interactions and local sparse relationship modeling. Third, we propose a novel multi-branch fusion module to integrate information from multiple sources and generate answer predictions. The proposed heterogeneous-branch integration framework outperforms the VDGN method by 2.73% in accuracy on the ReClor dataset and 2.15% on the LogiQA dataset. Our code and models will be made available at https://***/starry-y/HBI.

关键词： Question answering logical reasoning Graph transformer first-order predicate logic Propositional logic

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Coherence in linear predicate logic

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ANNALS OF PURE AND APPLIED logic 2009年第1-2期158卷 125-153页

作者： Dosen, Kosta Petric, Zoran SANU Math Inst Belgrade 11001 Serbia

Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic Without or with mix. To obtain this result, coherence is first established for categories that correspond to the multiplicative conjunction-disjunction fragment with first-order quantifiers of classical linear logic, a fragment lacking negation. These results extend results of [K. Dosen, Z. Petric, Proof-Theoretical Coherence, KCL Publications (College Publications), London, 2004 (revised version available at: http://***/similar to kosta/***): K. Dosen, Z. Petric, Proof-Net Categories, Polimetrica, Monza, 2007 (preprint available at: http://***/similar to kosta/***, 2005)], where coherence was established for categories of the corresponding fragments of propositional classical linear logic, which are related to proof nets, and which could be described as star-autonomous categories without unit objects. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Classical linear logic first-order predicate logic Proof-net category Coherence Criteria of identity for proofs Cut elimination

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Cut elimination inside a deep inference system for classical predicate logic

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Studia logica 2006年第1期82卷 51-71页

作者： Brünnler, Kai Institut für Angewandte Mathematik und Informatik CH - 3012 Bern Neubrückstr. 10 Switzerland

Deep inference is a natural generalisation of the one-sided sequent calculus where rules are allowed to apply deeply inside formulas, much like rewrite rules in term rewriting. This freedom in applying inference rules allows to express logical systems that are difficult or impossible to express in the cut-free sequent calculus and it also allows for a more fine-grained analysis of derivations than the sequent calculus. However, the same freedom also makes it harder to carry out this analysis, in particular it is harder to design cut elimination procedures. In this paper we see a cut elimination procedure for a deep inference system for classical predicate logic. As a consequence we derive Herbrand's Theorem, which we express as a factorisation of derivations. © Springer 2006.

关键词： Cut elimination Deep inference first-order predicate logic

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Embedding first-order logic in a pure type system with parameters

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JOURNAL OF logic AND COMPUTATION 2001年第4期11卷 545-557页

作者： Laan, T Franssen, M Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

A standard way to code first-order predicate logic in a propositions-as-types style uses a type system that is a variant of the pure type system AP. Types in this system are not necessarily in beta -normal form. Therefore, checking whether two types are beta -equal is decidable, albeit sometimes costly in terms of time and/or memory. In this paper we present an alternative to Berardi's system, based on pure type systems with parameters. We show that all types in our system are in beta -normal form, which is an advantage for implementations. Moreover, the syntactical structure of the system with parameters is similar to the syntax of first-order predicate logic. This is not the case for the system without parameters.

关键词： first-order predicate logic pure type systems type theory

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HCLIE - A logic-BASED REQUIREMENT LANGUAGE FOR NEW SOFTWARE ENGINEERING PARADIGMS

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SOFTWARE ENGINEERING JOURNAL 1991年第4期6卷 137-151页

作者： TSAI, JJP WEIGERT, T Department of Electrical Engineering and Computer Science University of Illinois Chicago USA

It is a paradigm of software engineering, which is especially popular among researchers involved in automatic programming, that a complete representation of the problem domain (called requirement theory) is repeatedly refined by correctness-preserving transformations into the program itself. The design of a requirement theory has to allow for such a design methodology. We argue that currently available languages intended to yield requirement theories fail to meet these demands. In this paper, we present a logic-based requirement language, which can be used to specify the requirements for software systems under the emerging methodology. The language presented here is based on first-order predicate logic but augments standard first-order logic by introducing hierarchies and exceptions to its generalisations, in order to allow for a more natural description of the problem domain. The proposed requirement language is valid and can be determined to be internally consistent. With the support of the requirement language, software development using new software engineering paradigms can be easily achieved.

关键词： HCLIE logic-based requirement language software engineering formal logic specification languages standard first-order logic first-order predicate logic Horn-Clause logic with Inheritance and Exception Prolog Software engineering techniques design methodology High level languages logic programming requirement theory

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logical and Algebraic View of Huzita's Origami Axioms with Applications to Computational Origami 07

Logical and Algebraic View of Huzita's Origami Axioms with A...

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22nd ACM Symposium on Applied Computing

作者： Ghourabi, Fadoua Ida, Tetsuo Takahashi, Hidekazu Marin, Mircea Kasem, Asem Univ Tsukuba Dept Comp Sci Tsukuba Ibaraki 3058573 Japan

ISBN: (纸本)9781595934802

We describe Huzita's origami axioms from the logical and algebraic points of view. Observing that Huzita's axioms are statements about the existence of certain origami constructions, we can generate basic origami constructions from those axioms. Origami construction is performed by repeated application of Huzita's axioms. We give the logical specification of Huzita's axioms as constraints among geometric objects of origami in the language of the first-order predicate logic. The logical specification is then translated into logical combinations of algebraic forms, i.e. polynomial equalities, disequalities and inequalities, and further into polynomial ideals (if inequalities are not involved). By constraint solving, we obtain solutions that satisfy the logical specification of the origami construction problem. The solutions include fold lines along which origami paper has to be folded. The obtained solutions both in numeric and symbolic forms make origami computationally tractable for further treatments, such as visualization and automated theorem proving of the correctness of the origami construction.

关键词： origami first-order predicate logic constraint solving geometric theorem proving

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