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Topic: Automated theorem proving

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HOL theorem prover

Proof theory

E equational theorem prover

Vampire theorem prover

Model checking

Complexity classes P and NP

Term rewriting

Logical argument

Logic

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	Automated theorem proving - Wikipedia, the free encyclopedia
		Automated theorem proving (currently the most important subfield of automated reasoning) is the proving of mathematical theorems by a computer program.
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs).
		First-order theorem proving is one of the most mature subfields of automated theorem proving.
	en.wikipedia.org /wiki/Automated_theorem_proving (1136 words)

	Automated theorem proving: Definition and Links by Encyclopedian.com - All about Automated theorem proving (Site not responding. Last check: 2007-11-05)
		Automated theorem proving is the process of getting a computer to agree that a particular theorem is true.
		In reality, there is no general-purpose system that can fully automatically prove "interesting" theorems, and most theorem proving systems can be used in a variety of ways with different amounts of automation, so this distinction is often dropped and both sides of the continuum are called theorem proving.
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to check by hand.
	www.encyclopedian.com /th/Theorem-prover.html (443 words)

	Encyclopedia: Automated theorem proving
		In automated theorem proving, Coq is a proof assistant which handles mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
		The Isabelle theorem prover is an interactive theorem proving framework, a successor of the HOL theorem prover.
		Theorem provers A computer-assisted proof is a mathematical proof that has been generated by computer.
	www.nationmaster.com /encyclopedia/Automated-theorem-proving (2858 words)

	Automated Development of Fundamental Mathematical Theories by Art Quaife
		A theorem has a bunch of sentences called its hypotheses, and a single sentence called its conclusion; what makes it a theorem is the existence of a proof that the conclusion follows from the hypotheses.
		The real work in proving a deep theorem lies in the development of the theory that it belongs to and its relationships to other theories, the design of definitions and axioms, the selection of good inference rules, and the recognition and proof of more basic theorems.
		It lacks the ability, surely a component of human approaches to proof, to reject purported theorems that are plainly false on semantic grounds (such as the use of symmetry or of diagrams in the case of geometry).
	psyche.cs.monash.edu.au /v2/psyche-2-28-fearnley_sande.html (3454 words)

	Automated theorem proving - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		Automated theorem proving (currently the most important subfield of) is the proving of mathematical theorems by a computer program.
		For first-order logic it is recursively enumerable, i.e., given unbounded resources, any true theorem can eventually be proven, but invalid theorems cannot always be recognized.
		A simpler, but related problem is, where an existing proof for a theorem is certified valid.
	www.leessummit.us /project/wikipedia/index.php/Automated_theorem_proving (645 words)

	Automated theorem proving - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-05)
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enourmous size of the program's calculation (such proofs are called non-surveyable proofs).
		Theorem Proving in Higher Order Logics : 14th International Conference, TPHOLs 2001, Edinburgh, Scotland, UK, September 3-6, 2001.
		Automated Deduction CADE-20 : 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005, Proceedings (Lecture Notes in...
	encyclopedia.worldsearch.com /automated_theorem_proving.htm (740 words)

	Read about Automated theorem proving at WorldVillage Encyclopedia. Research Automated theorem proving and learn about ... (Site not responding. Last check: 2007-11-05)
		recursively enumerable, i.e., given unbounded resources, any true theorem can eventually be proven, but invalid theorems cannot always be recognized.
		four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs).
		AMD, Intel, and others, automated theorem proving has been used to verify that the divide and other operations are correct.
	encyclopedia.worldvillage.com /s/b/Automated_theorem_proving (588 words)

	Automated Reasoning Group (Site not responding. Last check: 2007-11-05)
		The Automated Reasoning Group is concerned with the development and application of theorem proving methodologies.
		Use of theorem proving methods is finding substantial application with the increasing use of computers in safety-critical applications, whose workings require detailed analysis.
		Information on the HOL system for interactive theorem proving in a higher-order logic and Isabelle generic theorem prover is available.
	www.cl.cam.ac.uk /Research/HVG (196 words)

	AI Magazine: Automated Theorem Proving: Theory and Practice. - book review (Site not responding. Last check: 2007-11-05)
		Automated Theorem Proving (ATP) deals with the development of computer programs that show that some statement (the conjecture) is a logical consequence of a set of statements (the axioms and hypotheses).
		To build a useful ATP system, several issues have to carefully be considered, independently and in relation to each other, and addressed in a synergetic manner.
		Herbrand's theorem and the semantic tree calculus are presented in chapter 5.
	www.findarticles.com /p/articles/mi_m2483/is_1_23/ai_84804959 (1211 words)

	CL Seminar Oct 21 2004 (Site not responding. Last check: 2007-11-05)
		Automated Theorem Proving (ATP) is concerned with the development and use of systems that automate sound reasoning: the derivation of conclusions that follow inevitably from facts.
		While theorems in rich theories are often hard for an individual ATP system to prove, the richness provides sources of information and opportunities to use high level ATP techniques intelligent ways.
		The projects include analysis and selection of axioms for proving a given conjecture, the automatic generation and use of lemmas, cooperative competition between ATP systems, and semantic verification of proofs.
	www.cs.sfu.ca /~cl/seminars/abstracts/2004/Oct_21.htm (161 words)

	Automated theorem proving (Site not responding. Last check: 2007-11-05)
		Other techniques would include model checking[?], which is equivalent to brute-force enumeration of many possible states (although the actual implementation of model checkers requires much cleverness, and doesn't simply reduce to brute force).
		All is still licensed under the GNU FDL.
		I suggest that Congress create a commission to of opening to our citizens, under just and enduring conditions, the richly British Islands, by governmental or municipal aid, of persons unable.
	www.termsdefined.net /au/automated-theorem-proving.html (590 words)

	Automated Theorem Proving in Lattice-Ordered Structures (Site not responding. Last check: 2007-11-05)
		In the first part of the course we introduce some fundamental notions in automated theorem proving: we recall the main results in resolution and its refinements and in rewriting; then we present superposition and ordered chaining with selection.
		We show that the idea of using relational structures instead of algebras can also be applied to automated theorem proving in classes of distributive lattices with operators.
		We end with some applications to automated theorem proving in some classes of non-classical logics, especially (multi-)modal logics, intuitionistic logic, some many-valued logics.
	www.logic.at /lvas/185134 (264 words)

	Formal Mathematics and Automated Theorem Proving (Site not responding. Last check: 2007-11-05)
		Proved theorems form the basis of proved methods for solving problems by computer.
		However, currently, the process of inventing and proving individual theorems and the even more demanding process of exploring entire mathematical theories and of presenting such theories in a coherent form in text books and lecture notes, is hardly supported by the computer.
		It is well known that many non-trivial geometrical theorems, when represented in coordinates, have this form and, thus, can be proved automatically by this method.
	www.risc.uni-linz.ac.at /research/theorem (583 words)

	Automated Theorem Proving - Theory
		However, the emphasis of this section is to help the reader learn the basics and later use them to understand the high level overview of the theorem proving methods and development.
		Church and Turing in 1936 proved that is was impossible to find a general decision to verify the inconsistency of a formula.
		Since the emphasis of our project is automated theorem proving in a general sense, we will not discuss the details.
	cse.stanford.edu /classes/sophomore-college/projects-99/automatic-theorem-proving/theory.htm (2721 words)

	An Overview of Automated Theorem Proving
		This formality is the underlying strength of ATP: there is no ambiguity in the statement of the problem, as is often the case when using a natural language such as English.
		ATP is thus a technology very suited to situations where a clear thinking domain expert can interact with a powerful tool, to solve interesting and deep problems.
		Potential ATP users need not be concerned that they need to write an ATP system themselves; there are many ATP systems readily available for use.
	www.cs.miami.edu /~tptp/OverviewOfATP.html (1495 words)

	Automated theorem proving -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		Automated theorem proving (currently the most important subfield of automated reasoning) is the (Click link for more info and facts about proving) proving of mathematical (An idea accepted as a demonstrable truth) theorems by a computer program.
		For this, it is generally required that each individual proof step can be verified by a (Click link for more info and facts about primitive recursive function) primitive recursive function or program, and hence the problem is always decidable.
		Other techniques would include (Click link for more info and facts about model checking) model checking, which is equivalent to brute-force enumeration of many possible states (although the actual implementation of model checkers requires much cleverness, and does not simply reduce to brute force).
	www.absoluteastronomy.com /encyclopedia/a/au/automated_theorem_proving.htm (873 words)

	Automated Theorem Proving: Theory and Practice by Monroe Newborn [ISBN: 0387950753] - Find Cheap Textbook Prices & Save ... (Site not responding. Last check: 2007-11-05)
		As the 21st century begins, the power of our new tool and partner, the computer, is increasing at an astonishing rate.
		Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from facts, or abstractly, to prove theorems, the subject of this book.
		Anyone with an interest in automated reasoning will find the book an essential guide and hands-on tool for learning about the theorem-proving process.
	www.adultdvdmagic.com /isbn_0387950753.html (293 words)

	Review of book by Art Quaife (Site not responding. Last check: 2007-11-05)
		2.1 Mainstream automated theorem proving, to which Quaife's work belongs, is based on the method of resolution.
		2.3 A theorem has a bunch of sentences called its hypotheses, and a single sentence called its conclusion; what makes it a theorem is the existence of a proof that the conclusion follows from the hypotheses.
		2.5 What is required, then, to prove a theorem is to show that an associated set of sentences is unsatisfiable.
	www.maths.utas.edu.au /People/dfs/QuaifeReview.html (3452 words)

	Seminar in Automated Theorem Proving
		Automated (and semi-automated) theorem proving has been around for three decades.
		Either way, the science of automated proving is interesting for its own sake.
		Amy Felty, lambda Prolog and its Application to Theorem Proving, tutorial slides, 1997.
	www.cs.princeton.edu /~appel/proofsem (481 words)

	ICCL Summer School 2004
		The themes for the summer school are proof theory and automated theorem proving, the workshop is about proof, computation and complexity.
		This course concerns the application of automated reasoning techniques to logics broadly in the substructural family, such as linear logic, affine logic, relevant logic or the like.
		It is naturally easy, given a cut-free sequent calculus presentation with an algorithmic flavour of a system of logic, to generate a program that searches for proofs in the logic, and given a proof of termination for some fragment of the logic this generally yields a decision procedure for that fragment.
	www.iccl.tu-dresden.de /events/SA-2004 (1556 words)

	Mechanized Reasoning (Site not responding. Last check: 2007-11-05)
		To understand what automated reasoning is, we must first understand what reasoning is. Reasoning is the process of drawing conclusions from facts.
		The object of automated reasoning is to write computer programs that assist in solving problems and in answering questions requiring reasoning.
		You can use such a program in an iterative fashion; that is, you can instruct it to draw some conclusions and present them to you, and then, based on your analysis of the conclusions, it can in the next run execute your new set of instructions.
	www-formal.stanford.edu /clt/ARS/ars-db.html (375 words)

	Peter B. Andrews
		Potential applications of automated theorem proving include hardware and software verification, partial automation of various mathematical activities, promoting development of formal theories in a wide variety of disciplines, deductive information systems for these disciplines, expert systems which can reason, and certain aspects of artificial intelligence.
		The research is based on an approach to automated theorem proving involving expansion proofs and matings.
		A subsystem of TPS called ETPS (Educational Theorem Proving System) is used as an interactive aid in logic courses.
	gtps.math.cmu.edu /andrews.html (1135 words)

	15-815 Automated Theorem Proving: Project Week 5 (Site not responding. Last check: 2007-11-05)
		Besides consolidation, documentation, and evaluation, the groups concerned with the inverse method might consider how the ordering explicit in Tammet's strong inversion strategy may be applied in the inverse prover based on focusing sequents.
		This strategy is explained on pages 14 and 15 of the draft paper A Resolution Theorem Prover for Intuitionistic Logic by Tanel Tammet.
		No special individual assignments are made, except for consolidation, documentation, and evaluation of all components.
	www.lb.cs.cmu.edu /~fp/courses/99-atp/projects/week5.html (180 words)

	TPTP
		The TPTP (Thousands of Problems for Theorem Provers) Problem Library is a library of test problems for automated theorem proving (ATP) systems.
		A comprehensive library of the ATP test problems that are available today, in order to provide an overview and a simple, unambiguous reference mechanism.
		The principal motivation for the TPTP is to support the testing and evaluation of ATP systems, to help ensure that performance results accurately reflect the capabilities of the ATP system being considered.
	www.cs.miami.edu /~tptp (724 words)

	Automated theorem proving - Encyclopedia, History, Geography and Biography
		Automated theorem proving - Encyclopedia, History, Geography and Biography
		This page was last modified 17:39, 16 Jun 2005.
		The article about Automated theorem proving contains information related to Automated theorem proving, Popular techniques, Available implementations, Important people and References (books).
	www.arikah.com /encyclopedia/Automated_theorem_proving (631 words)

	A Computer-Based Tutor for Automated Theorem Proving (Site not responding. Last check: 2007-11-05)
		Principal goal of the project: To build a computer-based tutor to teach the mechanism of resolution theorem proving.
		AI students are taught about resolution theorem proving in a several of our courses, eg knowledge representation and inference, automated reasoning.
		Background Needed: Attendance at the automated reasoning and AI and education modules.
	www.inf.ed.ac.uk /teaching/courses/diss/props/023_bundy8.html (301 words)

	Links to other ATP pages (Site not responding. Last check: 2007-11-05)
		TPS is an automated theorem proving program for higher-order logic.
		IMPS is another theorem proving system which uses knowledge.
		Automated Reasoning Group at the University of Cambridge Computer Laboratory
	www.ma.utexas.edu /users/bshults/ATP/related-links.html (111 words)

	Automated Theorem Proving In High-Quality Software Design (ResearchIndex)
		Hence, one aim of KIV's developers is to use automated theorem provers to process simple proof tasks without user interaction.
		To this end, the prover 3 T A P (H ahnle et al., 1992; H ahnle, 1993; Beckert and H ahnle, 1992) was integrated into KIV, and experiments on the expected performance of Setheo, SPASS, Otter, and Protein (Baumgartner and...
		9 Parallel Automated Theorem Proving (context) - Suttner, Schumann - 1993
	citeseer.ist.psu.edu /324342.html (1134 words)

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