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Expressing Set Theory in FirstOrder Predicate Logic
, 2000
"... Here we present a firstorder formalization of set theory that has a finite number of axioms and which syntax is similar to the one often used in books: it provides an encoding of the comprehension symbol. Other formalizations of set theory exist: Zermelo theory with existence axioms is firstorder ..."
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Here we present a firstorder formalization of set theory that has a finite number of axioms and which syntax is similar to the one often used in books: it provides an encoding of the comprehension symbol. Other formalizations of set theory exist: Zermelo theory with existence axioms is firstorder
Translating the Object Constraint Language into Firstorder Predicate Logic
 In Proceedings, VERIFY, Workshop at Federated Logic Conferences (FLoC
, 2002
"... In this paper, we define a translation of UML class diagrams with OCL constraints into firstorder predicate logic. The goal is logical reasoning about UML models, realized by an interactive theorem prover. We put an emphasis on usability of the formulas resulting from the translation, and we hav ..."
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Cited by 40 (6 self)
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In this paper, we define a translation of UML class diagrams with OCL constraints into firstorder predicate logic. The goal is logical reasoning about UML models, realized by an interactive theorem prover. We put an emphasis on usability of the formulas resulting from the translation, and we
Binary decision diagrams for first order predicate logic
 JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING 57:1–22
, 2003
"... We present an extension of Binary Decision Diagrams (BDDs) such that they can be used for predicate logic. We present a sound and complete proof search method which we apply to a number of examples. ..."
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Cited by 8 (0 self)
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We present an extension of Binary Decision Diagrams (BDDs) such that they can be used for predicate logic. We present a sound and complete proof search method which we apply to a number of examples.
DT  An Automated Theorem Prover for MultipleValued FirstOrder Predicate Logics
 IN PROC. 26TH INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGICS
, 1996
"... We describe the automated theorem prover "Deep Thought" ( d DT ). The prover can be used for arbitrary multiplevalued firstorder logics, provided the connectives can be defined by truth tables and the quantifiers are generalizations of the classical universal resp. existential quantifie ..."
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Cited by 2 (0 self)
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quantifiers. d DT has been tested with many interesting multiplevalued logics as well as classical firstorder predicate logic. d DT uses a freevariable semantic tableau calculus with generalized signs. For the existential tableaurules two liberalized versions are implemented. The system utilizes a static
Charaterising ObjectBased Frameworks in FirstOrder Predicate Logic
"... In the componentbased approach Catalysis, a framework is a reusable artefact that can be adapted and composed into larger systems. The signed contract between components specifies how the required properties of one component are satisfied by the provided properties of another. We examine this conce ..."
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this concept in the context of frameworkbased development. Although Catalysis advocates rigorous development, frameworks lack a comprehensive formal foundation. We consider a simplified view of frameworks and their transformation into firstorder logic. Theorem proving may be used to check the consistency
ILPbased Inference for Costbased Abduction on Firstorder Predicate Logic
"... Abduction is desirable for many natural language processing (NLP) tasks. While recent advances in largescale knowledge acquisition warrant applying abduction with large knowledge bases to reallife NLP problems, as of yet, no existing approach to abduction has achieved the efficiency necessary to ..."
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to be a practical solution for largescale reasoning on reallife problems. In this paper, we propose an efficient solution for largescale abduction. The contributions of our study are as follows: (i) we propose an efficient method of costbased abduction in rstorder predicate logic that avoids
A Domainindependent System for Modeling Number Theory Using FirstOrder Predicate Logic
, 1999
"... Many existing theorem provers employ domaindependent knowledge in their aim to model the reasoning methods of mathematics. In hoping to achieve the same objective, yet in a better way, the present work seeks to provide a domainindependent system of theorems for modeling number theory using firsto ..."
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Many existing theorem provers employ domaindependent knowledge in their aim to model the reasoning methods of mathematics. In hoping to achieve the same objective, yet in a better way, the present work seeks to provide a domainindependent system of theorems for modeling number theory using firstorder
Lecture 4: Syntax and Semantics of Predicate Logic, Continued. Semantics of Adjectives and Relative Clauses. Limitations of FirstOrder Predicate Logic for Natural Language Semantics. Handouts for today: BACKGROUND material: Basic Concepts of Set Theory,
"... More Answers for Practice in Logic and HW1 (an expanded version of the handout I put the 310 cubbyhole on Monday afternoon) This handout. We will also refer to some parts of the handout from Lecture 2. 1. Syntax and semantics of Predicate Calculus, continued. For the first part, we will primarily ..."
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More Answers for Practice in Logic and HW1 (an expanded version of the handout I put the 310 cubbyhole on Monday afternoon) This handout. We will also refer to some parts of the handout from Lecture 2. 1. Syntax and semantics of Predicate Calculus, continued. For the first part, we
International Journal of Pattern Recognition and Artificial Intelligence c ○ World Scientific Publishing Company A FIRST ORDER PREDICATE LOGIC FORMULATION OF THE 3D RECONSTRUCTION PROBLEM AND ITS SOLUTION SPACE
"... This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is illposed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solutio ..."
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reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using
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