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Generating Plans From Proofs
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Book Synopsis Generating Plans from Proofs by : Michael Benedikt
Download or read book Generating Plans from Proofs written by Michael Benedikt and published by Morgan & Claypool Publishers. This book was released on 2016-03-15 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Query reformulation refers to a process of translating a source query—a request for information in some high-level logic-based language—into a target plan that abides by certain interface restrictions. Many practical problems in data management can be seen as instances of the reformulation problem. For example, the problem of translating an SQL query written over a set of base tables into another query written over a set of views; the problem of implementing a query via translating to a program calling a set of database APIs; the problem of implementing a query using a collection of web services. In this book we approach query reformulation in a very general setting that encompasses all the problems above, by relating it to a line of research within mathematical logic. For many decades logicians have looked at the problem of converting "implicit definitions" into "explicit definitions," using an approach known as interpolation. We will review the theory of interpolation, and explain its close connection with query reformulation. We will give a detailed look at how the interpolation-based approach is used to generate translations between logic-based queries over different vocabularies, and also how it can be used to go from logic-based queries to programs.
Book Synopsis Generating Plans from Proofs by : Michael Benedikt
Download or read book Generating Plans from Proofs written by Michael Benedikt and published by Springer Nature. This book was released on 2022-06-01 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Query reformulation refers to a process of translating a source query—a request for information in some high-level logic-based language—into a target plan that abides by certain interface restrictions. Many practical problems in data management can be seen as instances of the reformulation problem. For example, the problem of translating an SQL query written over a set of base tables into another query written over a set of views; the problem of implementing a query via translating to a program calling a set of database APIs; the problem of implementing a query using a collection of web services. In this book we approach query reformulation in a very general setting that encompasses all the problems above, by relating it to a line of research within mathematical logic. For many decades logicians have looked at the problem of converting "implicit definitions" into "explicit definitions," using an approach known as interpolation. We will review the theory of interpolation, and explain its close connection with query reformulation. We will give a detailed look at how the interpolation-based approach is used to generate translations between logic-based queries over different vocabularies, and also how it can be used to go from logic-based queries to programs.
Book Synopsis Generating Plans From Proofs: The Interpolation-based Approach to Query Reformulation by : Efthymia Tsamoura
Download or read book Generating Plans From Proofs: The Interpolation-based Approach to Query Reformulation written by Efthymia Tsamoura and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Plan Generation by Linear Proofs by :
Download or read book Plan Generation by Linear Proofs written by and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Building Proofs written by Suely Oliveira and published by World Scientific Publishing Company. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level. Just beyond the standard introductory courses on calculus, theorems and proofs become central to mathematics. Students often find this emphasis difficult and new. This book is a guide to understanding and creating proofs. It explains the standard "moves" in mathematical proofs: direct computation, expanding definitions, proof by contradiction, proof by induction, as well as choosing notation and strategies.
Download or read book Proof Planning written by Alan Bundy and published by . This book was released on 1998 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans constructed by plan formation techniques. Some differences are the non-persistence of objects in the mathematical domain, the absence of goal interaction in mathematics, the high degree of generality of proof plans, the use of a meta-logic to describe preconditions in proof planning and the use of annotations in formulae to guide search."
Book Synopsis Plan generation by linear proofs by :
Download or read book Plan generation by linear proofs written by and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Planning Mathematical Proofs with Methods by :
Download or read book Planning Mathematical Proofs with Methods written by and published by . This book was released on 1994 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generating Plans from Proofs by : Michael Benedikt
Download or read book Generating Plans from Proofs written by Michael Benedikt and published by Springer. This book was released on 2016-03-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Query reformulation refers to a process of translating a source query—a request for information in some high-level logic-based language—into a target plan that abides by certain interface restrictions. Many practical problems in data management can be seen as instances of the reformulation problem. For example, the problem of translating an SQL query written over a set of base tables into another query written over a set of views; the problem of implementing a query via translating to a program calling a set of database APIs; the problem of implementing a query using a collection of web services. In this book we approach query reformulation in a very general setting that encompasses all the problems above, by relating it to a line of research within mathematical logic. For many decades logicians have looked at the problem of converting "implicit definitions" into "explicit definitions," using an approach known as interpolation. We will review the theory of interpolation, and explain its close connection with query reformulation. We will give a detailed look at how the interpolation-based approach is used to generate translations between logic-based queries over different vocabularies, and also how it can be used to go from logic-based queries to programs.
Book Synopsis Planning Mathematical Proofs with Methods by :
Download or read book Planning Mathematical Proofs with Methods written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Use of Explicit Plans to Guide Inductive Proofs by : Alan Bundy
Download or read book The Use of Explicit Plans to Guide Inductive Proofs written by Alan Bundy and published by . This book was released on 1987 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proof Plans for the Correction of False Conjectures by : Raul Monroy
Download or read book Proof Plans for the Correction of False Conjectures written by Raul Monroy and published by . This book was released on 1994 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Theorem proving is the systematic derivation of a mathematical proof from a set of axioms by the use of rules of inference. We are interested in a related but far less explored problem: the analysis and correction of false conjectures, especially where that correction involves finding a collection of antecedents that, together with a set of axioms, transform non-theorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenomenon. Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct non-theorems."
Book Synopsis Proof Plans and Automatic Theorem Proving with Hints by : Santiago Negrete
Download or read book Proof Plans and Automatic Theorem Proving with Hints written by Santiago Negrete and published by . This book was released on 1993 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In mathematical text we often find exercises in which the author gives the student some hints to help him or her solve the hard steps of a proof. In this paper, we present the design and use of a system that allows us to incorporate hints in Automatic Theorem Proving in the context of the Proof Plans paradigm. This technique, developed by the Mathematical Reasoning Group at AI department, University of Edinburgh, consists of the generation of a proof plan from abstract specifications of proof techniques applicable in Proof Editors. The system introduced here allows us to incorporate the use of hints to generate proof plans in Clam, an implementation of Proof Plans used to proof theorems in Martin-Löf's type theory. The use of hints in Clam improves considerably its capacity as a development and experimentation environment for automatic theorem proving techniques."
Book Synopsis Formulas for Generating Plans by : Sharon Sickel
Download or read book Formulas for Generating Plans written by Sharon Sickel and published by . This book was released on 1977 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: A closed form is discussed that provides an interface between formal specification of problems and the algorithms that solve them. (Author).
Book Synopsis Additive Deductive Embeddings for Planning of Natural Language Proofs by : Zayne Sprague
Download or read book Additive Deductive Embeddings for Planning of Natural Language Proofs written by Zayne Sprague and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructing a logical argument to support a claim entails selecting relevant evidence from a collection of facts and formulating a sequence of reasoning steps. Current natural language systems designed for claim validation employ large language models to reason and plan deductions. In this paper, we investigate whether embedding spaces can adequately represent natural language deductions for use in proof-generating systems. We introduce a novel method for planning natural language proof generation called Additive Deduction, which leverages simple arithmetic operations performed exclusively in an embedding space. We explore multiple sources of off-the-shelf dense embeddings in addition to sparse embeddings from BM25. We devise three experiments to demonstrate the effectiveness of embedding models for natural language planning. The first experiment consists of two intrinsic evaluations of Additive Deduction using two off-the-shelf sentence encoders. The second incorporates an embedding-based heuristic into planning for natural language proof generation datasets, namely EntailmentBank and Everyday Norms: Why Not. Lastly, we create a dataset that benchmarks various reasoning categories and common reasoning failures. Our findings suggest that while standard embedding methods frequently embed conclusions near the sums of their premises, they lack the ability to fully express certain categories of reasoning, hurting their proof generation performance
Book Synopsis Automated Deduction - CADE-19 by : Franz Baader
Download or read book Automated Deduction - CADE-19 written by Franz Baader and published by Springer Science & Business Media. This book was released on 2003-07-16 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed proceedings of the 19th International Conference on Automated Deduction, CADE 2003, held in Miami Beach, FL, USA in July 2003. The 29 revised full papers and 7 system description papers presented together with an invited paper and 3 abstracts of invited talks were carefully reviewed and selected from 83 submissions. All current aspects of automated deduction are discussed, ranging from theoretical and methodological issues to the presentation of new theorem provers and systems.
Book Synopsis Book of Proof by : Richard H. Hammack
Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
