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Discovery and Reasoning in Mathematics

1985
*
International Joint Conference on Artificial Intelligence
*

We discuss the automation of mathematical reasoning, surveying the abilities displayed by human mathematicians and the computational techniques available

dblp:conf/ijcai/Bundy85
fatcat:nfwo4w6rajb7djr72pwbje4b3i
*for*automating these abilities. ... Automated*theorem**proving*has been an important subfield of AI throughout its history. The main techniques required to automate*theorem**proving*are deduction which involves*search**control*. ... -The IMPRESS (Inferring Meta-*knowledge*about PRESS) program, [Sterling & Bundy 82], was a*theorem**proving*program*for**proving*properties of logic programs. ...##
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Automatic Acquisition of Search Control Knowledge from Multiple Proof Attempts

2000
*
Information and Computation
*

We present two inference

doi:10.1006/inco.1999.2857
fatcat:u2iletlydng47ievjcsiiftr6e
*control*heuristics*for**equational*deduction that are based on the evaluation of previous successful proof attempts in domains of interest. ... The first evaluation function works by symbolic retrieval of generalized patterns from a*knowledge*base, and the second function compiles the*knowledge*into abstract term evaluation trees. ... AddWeight and extensions of it provide a good basis*for**learning*approaches to*control*the*search*of a*theorem*prover. ...##
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Learning domain knowledge to improve theorem proving
[chapter]

1996
*
Lecture Notes in Computer Science
*

We present two

doi:10.1007/3-540-61511-3_69
fatcat:qh5stt4rfzdevepn27rbda5rku
*learning*inference*control*heuristics*for**equational*deduction. ... Based on data about facts that contributed to previous proofs, evaluation functions*learn*to select*equations*that are likely to be of use in new situations. ... The task of*learning*heuristics*for**theorem*provers is highly non-trivial. The rst problem is the selection of the choice points to be*controlled*by a*learning*heuristic. ...##
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High Performance ATP Systems by Combining Several AI Methods

1997
*
International Joint Conference on Artificial Intelligence
*

We present a design

dblp:conf/ijcai/DenzingerFF97
fatcat:nkuorq2wb5h6lem4m5zl3trlui
*for*an automated*theorem*prover that*controls*its*search*based on ideas from several areas of artificial intelligence (AI). ... We provide case studies from two domains in pure*equational**theorem**proving*. ... and to use*control**knowledge*. ...##
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Page 447 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

geometry

*theorem**proving*. ... (English summary) [*Learning*rules*for*feedback*control*laws*for*state constrained problems] C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 6, 445-450. ...##
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Combining theorem proving and symbolic mathematical computing
[chapter]

1995
*
Lecture Notes in Computer Science
*

We describe a model

doi:10.1007/3-540-60156-2_3
fatcat:gptoyfozcnb73kgiy6mwgus46m
*for*such a*knowledge*base mainly consisting of type and algorithm schemata, algebraic algorithms and*theorems*. ... A high level of interaction requires a common*knowledge*representation of the mathematical*knowledge*of the two systems. ... and*learning*of*theorems*out of algebraic algorithms, generation of algorithms from*theorems*, interaction of the*learning*component and the*theorem*prover and applications of the environment. ...##
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Neural dynamic optimization for control systems.II. Theory

2001
*
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)
*

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback

doi:10.1109/3477.938255
pmid:18244816
fatcat:lv5pihup35eulacrqgt3zkmeaa
*control**for*nonlinear multi-input-multi-output (MIMO) systems. ... Index Terms-Dynamic programming, information time shift operator,*learning*operator, neural dynamic optimization, neural networks, nonlinear systems, optimal feedback*control*. ...*Learning*Operator In this section, we introduce the*learning*operator, which characterizes the*learning*process of the neural network in*searching**for*the optimal feedback solution. ...##
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Proof planning with multiple strategies

2008
*
Artificial Intelligence
*

Proof planning is a technique

doi:10.1016/j.artint.2007.11.004
fatcat:g4keqaoqjjartcaufcspbv3fz4
*for**theorem**proving*which replaces the ultra-efficient but blind*search*of classical*theorem**proving*systems by an informed*knowledge*-based planning process that employs mathematical ...*knowledge*at a human-oriented level of abstraction. ... We are grateful*for*this substantial funding that made this work possible. ...##
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Computer supported mathematics with Ωmega

2006
*
Journal of Applied Logic
*

Classical automated

doi:10.1016/j.jal.2005.10.008
fatcat:bfpsfvprmnfnddfvwwx5cqbjiq
*theorem**proving*of today is based on ingenious*search*techniques to find a proof*for*a given*theorem*in very large*search*spaces-often in the range of several billion clauses. ... The shift from*search*based methods to more abstract planning techniques however opened up a paradigm*for*mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive ... Secondly, there is mathematical*knowledge*on how to*prove*a*theorem*, which is encoded in tactics and methods, in ANTS agents, in*control**knowledge*and in strategies. ...##
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A robust line search for learning control

2001
*
International Journal of Control
*

In this paper a new line

doi:10.1080/00207170010025285
fatcat:volndvxqmnecllcmhmihxtcvci
*search**for*a Newton Rhapson*learning**control*algorithm is presented. ... It is shown that the answer is generally no, at least*for*gradient-based*learning**control*algorithms. ... On the Robustness Against Erroneous Constraint Jacobean of a New Line*Search**for*a Newton Rhaphson*Learning**Control*Algorithm This section will*prove*that the modifiedline-*search*Newton Rhaphson algorithm ...##
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Strategic Issues, Problems and Challenges in Inductive Theorem Proving

2005
*
Electronical Notes in Theoretical Computer Science
*

Typically, (Automated)

doi:10.1016/j.entcs.2005.01.006
fatcat:reml2iecwfexhlnmr4d22a7sj4
*Theorem**Proving*(TP) refers to methods, techniques and tools*for*automatically*proving*general (most often first-order)*theorems*. ... Automated) Inductive*Theorem**Proving*(ITP) is a challenging field in automated reasoning and*theorem**proving*. ... I'm very grateful to Maria Paola Bonacina and Thierry Boy de la Tour, the Program Co-Chairs of STRATEGIES 2004,*for*this kind invitation and*for*their helpful comments on a draft version of this paper. ...##
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When to prove theorems by analogy?
[chapter]

1996
*
Lecture Notes in Computer Science
*

In recent years several computational systems and techniques

doi:10.1007/3-540-61708-6_66
fatcat:kyh4djijofc3zfvxdbghf5o2qi
*for**theorem**proving*by analogy have been developed. ... This paper addresses this question, identi es situations where analogy is useful, and discusses the merits of*theorem**proving*by analogy in these situations. ... Thanks to J org Siekmann and Wolf Schaarschmidt*for*reading drafts of this paper. ...##
###
Ωmega: Computer Supported Mathematics
[chapter]

2004
*
Lecture Notes in Computer Science
*

Classical

doi:10.1007/978-3-540-30221-6_2
fatcat:ez4gahurujebriliwvbo6ywxue
*theorem**proving*procedures of today are based on ingenious*search*techniques to find a proof*for*a given*theorem*in very large*search*spaces -often in the range of several billion clauses. ... While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof*for*a*theorem*by automatic means, the Automath project of N.G. de Bruijn 1 -more ... Secondly, there is mathematical*knowledge*on how to*prove*a*theorem*, which is encoded in tactics and methods, in ΩAnts agents, in*control**knowledge*and in strategies. ...##
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Reductio ad Absurdum: Planning Proofs by Contradiction
[chapter]

2006
*
Lecture Notes in Computer Science
*

Proof planning is a general technique in automated

doi:10.1007/11829263_3
fatcat:u6wtqxtd2ncnhdsc4rnfselhqm
*theorem**proving*that captures and makes explicit proof patterns and mathematical*search**control*. ... Sometimes it is pragmatically useful to*prove*a*theorem*by contradiction rather than finding a direct proof. ... mathematical*control**knowledge*in automated*theorem**proving*based on proof planning. ...##
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ΩMEGA: Resource-Adaptive Processes in an Automated Reasoning System
[chapter]

2010
*
Resource-Adaptive Cognitive Processes
*

The motivation is to reduce the combinatorial explosion of the

doi:10.1007/978-3-540-89408-7_17
dblp:series/cogtech/AutexierBDS11
fatcat:t6vlyxgwcbe45ctq7oy3mlb7sy
*search*space in classical automated*theorem**proving*by providing means*for*a more global*search**control*. ... or*control**knowledge*to restrict the*search*. ...
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