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12
Nonresolution theorem proving
 Artificial Intelligence
, 1977
"... This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplific ..."
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Cited by 60 (3 self)
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This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplification, builtin associativity and commutativity, models, analogy, and manmachine systems. Examples are given and suggestions are made for future work. 1.
NonStandard Analysis in ACL2
, 2001
"... ACL2 refers to a mathematical logic based on applicative Common Lisp, as well as to an automated theorem prover for this logic. The numeric system of ACL2 reflects that of Common Lisp, including the rational and complexrational numbers and excluding the real and complex irrationals. In conjunction ..."
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Cited by 20 (7 self)
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ACL2 refers to a mathematical logic based on applicative Common Lisp, as well as to an automated theorem prover for this logic. The numeric system of ACL2 reflects that of Common Lisp, including the rational and complexrational numbers and excluding the real and complex irrationals. In conjunction with the arithmetic completion axioms, this numeric type system makes it possible to prove the nonexistence of specific irrational numbers, such as √2. This paper describes ACL2(r), a version of ACL2 with support for the real and complex numbers. The modifications are based on nonstandard analysis, which interacts better with the discrete flavor of ACL2 than does traditional analysis.
A Combination of Nonstandard Analysis and Geometry Theorem Proving, with Application to Newton's Principia
 PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION (CADE15
, 1998
"... The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolutely geometric in nature but contains "infinitesimal" elements and the presence of motion that take it beyond the traditio ..."
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Cited by 10 (3 self)
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The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolutely geometric in nature but contains "infinitesimal" elements and the presence of motion that take it beyond the traditional boundaries of Euclidean Geometry. These present difficulties that prevent Newton's proofs from being mechanised using only the existing geometry theorem proving (GTP) techniques. Using
The Use of a Formal Simulator to Verify a Simple Real Time Control Program
 In Beauty Is Our Business
, 1990
"... We present an initial and elementary investigation of the formal specification and mechanical verification of programs that interact with environments. We describe a formal, mechanically produced proof that a simple, real time control program keeps a vehicle on a straightline course in a variable cr ..."
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Cited by 8 (4 self)
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We present an initial and elementary investigation of the formal specification and mechanical verification of programs that interact with environments. We describe a formal, mechanically produced proof that a simple, real time control program keeps a vehicle on a straightline course in a variable crosswind. To formalize the specification we define a mathematical function which models the interaction of the program and its environment. We then state and prove two theorems about this function: the simulated vehicle never gets farther than three units away from the intended course and homes to the course if the wind ever remains steady for at least four sampling intervals.
On the Mechanization of Real Analysis in Isabelle/HOL
"... Our recent, and still ongoing, development of real analysis in Isabelle/HOL is presented and compared, whenever instructive, to the one present in the theorem prover HOL. While most existing mechanizations of analysis only use the classical and approach, ours uses notions from both Nonstandard ..."
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Cited by 6 (0 self)
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Our recent, and still ongoing, development of real analysis in Isabelle/HOL is presented and compared, whenever instructive, to the one present in the theorem prover HOL. While most existing mechanizations of analysis only use the classical and approach, ours uses notions from both Nonstandard Analysis and classical analysis. The overall result is an intuitive, yet rigorous, development of real analysis, and a relatively high degree of proof automation in many cases.
SET VARIABLES
"... ABSTRACT: A procedure is described that gives values to set variables in automatic theorem proving. The result is that a theorem is thereby reduced to first order logic, which is often much easier to prove. This procedure handles a part of higher order logic, a small but important part. It is not as ..."
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Cited by 1 (0 self)
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ABSTRACT: A procedure is described that gives values to set variables in automatic theorem proving. The result is that a theorem is thereby reduced to first order logic, which is often much easier to prove. This procedure handles a part of higher order logic, a small but important part. It is not as general as the methods of Huet, Andrews, Pietrzykowski, and Haynes and Henschen, but it seems to be much faster when it applies. It is more in the spirit of J.L. Darlington's FMatching. This procedure is not domain specific: results have been obtained In intermediate analysis (the intermediate value theorem), topology, logic, and program verification (finding internal assertions). This method is a &quot;maximal method&quot; in that a largest (or maximal) set is usually produced if there is one. A preliminary version has been programmed for the computer and run to prove several theorems.
Axiomatic Events in ACL2(r): A Story of defun, defunstd, and encapsulate
, 2004
"... ACL2(r) is a variant of ACL2 that has support for reasoning about the real and complex numbers. It is based on the logic of nonstandard analysis, axiomatized by Nelson as an extension of ZF set theory [7, 6]. ACL2(r) is described in [2, 3]. This paper lays out the logical foundations of ACL2(r). 1 ..."
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ACL2(r) is a variant of ACL2 that has support for reasoning about the real and complex numbers. It is based on the logic of nonstandard analysis, axiomatized by Nelson as an extension of ZF set theory [7, 6]. ACL2(r) is described in [2, 3]. This paper lays out the logical foundations of ACL2(r). 1