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Computational Representations of Herbrand Models Using Grammars
 Computer Science Logic, 10th International Workshop, CSL'96, volume 1258 of LNCS
, 1997
"... . Finding computationally valuable representations of models of predicate logic formulas is an important subtask in many fields related to automated theorem proving, e.g. automated model building or semantic resolution. In this article we investigate the use of contextfree languages for representin ..."
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. Finding computationally valuable representations of models of predicate logic formulas is an important subtask in many fields related to automated theorem proving, e.g. automated model building or semantic resolution. In this article we investigate the use of contextfree languages for representing single Herbrand models, which appear to be a natural extension of "linear atomic representations" already known from the literature. We focus on their expressive power (which we find out to be exactly the finite models) and on algorithmic issues like clause evaluation and equivalence test (which we solve by using a resolution theorem prover), thus proving our approach to be an interesting base for investigating connections between formal language theory and automated theorem proving and model building. 1 Introduction Representing single models of predicate logic formulas plays an important role in various subfields of automated theorem proving. We just mention two of them: 1. An interesti...
Variational Attribute Grammars for Computer Aided Design (Release 3.0)
, 1994
"... This document describes a variational attribute grammar (VAG) design language and release 3.0 of the VAG implementation. VAG is a functional programming language specifically designed for the rapid implementation of domain specific CAD systems. VAG is intended to support the implementations of CAD ..."
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Cited by 4 (0 self)
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This document describes a variational attribute grammar (VAG) design language and release 3.0 of the VAG implementation. VAG is a functional programming language specifically designed for the rapid implementation of domain specific CAD systems. VAG is intended to support the implementations of CAD systems in such diverse areas as mechanical, electrical, and software design. The main feature of the VAG language is a constraint based reasoning mechanisms to support the CAD user in analyzing partial designs in a wide variety of domains. Release 3.0 provides a justification mechanism  no such mechanisms were provided in earlier releases.
Egeneralization using grammars
 ARTIFICIAL INTELLIGENCE JOURNAL
, 2005
"... We extend the notion of antiunification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of Egeneralization sets. We present a framework to combine Inductive Logic Programming and Egeneralization that includes an extension of Plot ..."
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We extend the notion of antiunification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of Egeneralization sets. We present a framework to combine Inductive Logic Programming and Egeneralization that includes an extension of Plotkin’s lgg theorem to the equational case. We demonstrate the potential power of Egeneralization by three example applications: computation of suggestions for auxiliary lemmas in equational inductive proofs, computation of construction laws for given term sequences, and learning of screen editor command sequences.
The Creation and Use of a Knowledge Base of Mathematical Theorems and Definitions
, 1995
"... IPR is an automatic theoremproving system intended particularly for use in higherlevel mathematics. It discovers the proofs of theorems in mathematics applying known theorems and definitions. Theorems and definitions are stored in the knowledge base in the form of sequents rather than formulas or ..."
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IPR is an automatic theoremproving system intended particularly for use in higherlevel mathematics. It discovers the proofs of theorems in mathematics applying known theorems and definitions. Theorems and definitions are stored in the knowledge base in the form of sequents rather than formulas or rewrite rules. Because there is more easilyaccessible information in a sequent than there is in the formula it represents, a simple algorithm can be used to search the knowledge base for the most useful theorem or definition to be used in the theoremproving process. This paper describes how the sequents in the knowledge base are formed from theorems stated by the user and how the knowledge base is used in the theoremproving process. An example of a theorem proved and the English proof output are also given. 1 Introduction The motivating goal behind this work is to develop a theoremproving system which will be useful to both an expert and a nonexpert in the attempt to prove theorems in ...
A Framework for Using Knowledge in Tableau Proofs
 Proc. International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, PontMousson
, 1997
"... . The problem of automatically reasoning using a knowledge base containing axioms, definitions and theorems from a firstorder theory is recurrent in automated reasoning research. Here we present a sound and complete method for reasoning over an arbitrary firstorder theory using the tableau cal ..."
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. The problem of automatically reasoning using a knowledge base containing axioms, definitions and theorems from a firstorder theory is recurrent in automated reasoning research. Here we present a sound and complete method for reasoning over an arbitrary firstorder theory using the tableau calculus. A natural, wellmotivated and simple restriction (implemented in IPR) to the method provides a powerful framework for the automation of the selection of theorems from a knowledge base for use in theorem proving. The restrictions are related to semantic resolution restrictions and the setofsupport restriction in resolution, and to hypertableaux and the weak connection condition in tableaux. We also present additional tableau rules used by the IPR prover for handling some equality which is not complete but is sufficient for handling the problems in its intended domain of problem solving. 1 Introduction The rules presented in this paper allow an automatic theorem proving pro...
Weight Computation of Regular Tree Languages
 Journal of Applied Logic
, 2004
"... We present a general framework to define an applicationdependent weight measure on terms that subsumes e.g. total simplification orderings, and an O(n log n) algorithm for the simultaneous computation of the minimal weight of a term in the language of each nonterminal of a regular tree grammar, b ..."
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We present a general framework to define an applicationdependent weight measure on terms that subsumes e.g. total simplification orderings, and an O(n log n) algorithm for the simultaneous computation of the minimal weight of a term in the language of each nonterminal of a regular tree grammar, based on Barzdins' liquidflow technique.
Variational Attribute Grammars for Computer Aided Design (Release 3.0)
"... : This document describes a variational attribute grammar (VAG) design language and release 3.0 of the VAG implementation. VAG is a functional programming language specifically designed for the rapid implementation of domain specific CAD systems. VAG is intended to support the implementations of CAD ..."
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: This document describes a variational attribute grammar (VAG) design language and release 3.0 of the VAG implementation. VAG is a functional programming language specifically designed for the rapid implementation of domain specific CAD systems. VAG is intended to support the implementations of CAD systems in such diverse areas as mechanical, electrical, and software design. The main feature of the VAG language is a constraint based reasoning mechanisms to support the CAD user in analyzing partial designs in a wide variety of domains. Release 3.0 provides a justification mechanism  no such mechanisms were provided in earlier releases. 1 1 Introduction This document, ADAGEMIT9402, is largely identical to the earlier document MITADAGE9401. The differences involve the justification mechasisms provided in release 3.0 of the software. These mechanisms are not provided in eariler releases. The new mechanisms are described in section 4. VAG is a functional programming language de...