D.B. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD thesis, Stanford University, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....et al., and the HR program which works mainly with finite algebras. For clarity, no other programs are discussed. 2. 1 The AM Program The AM program, written by Douglas Lenat, performed concept formation and conjecture making in elementary set theory and elementary number theory, as described in Lenat (1976) and Davis and Lenat (1982) Starting with 115 elementary concepts such as sets and bags, AM would re invent set theory concepts like subsets and disjoint sets, and number theory concepts such as prime numbers and highly composite numbers (with more divisors than any smaller integer) AM would ....

....which works mainly with finite algebras. For clarity, no other programs are discussed. 2. 1 The AM Program The AM program, written by Douglas Lenat, performed concept formation and conjecture making in elementary set theory and elementary number theory, as described in Lenat (1976) and Davis and Lenat (1982) Starting with 115 elementary concepts such as sets and bags, AM would re invent set theory concepts like subsets and disjoint sets, and number theory concepts such as prime numbers and highly composite numbers (with more divisors than any smaller integer) AM would also spot some well ....

[Article contains additional citation context not shown here]

D Lenat. AM: An artificial intelligence approach to discovery in mathematics. PhD thesis, Stanford University, 1976.

....new formula for : 1 X i=0 1 16 i 4 8i 1 Gamma 2 8i 4 Gamma 1 8i 5 Gamma 1 8i 6 : 2. 1 The AM Program The AM program, written by Douglas Lenat, performed concept formation and conjecture making in elementary set and number theory, as described in [7] and [21]. Starting with 115 elementary concepts such as sets and bags, AM would re invent set theory concepts like subsets and disjoint sets, and number theory concepts such as prime numbers and highly composite numbers (with more divisors than any smaller integer) AM would also spot some well known ....

D Lenat. AM: An artificial intelligence approach to discovery in mathematics. PhD thesis, Stanford University, 1976.

....on the eventual use of acquired knowledge. For, example, most concept acquisition systems are designed to acquire knowledge dedicated to performing classification, applying the acquired definitions of the target concepts to unclassified instance descriptions. 4 4 One notable exception is AM [Len76] which learned by discovering new concepts in the domain of mathematics. In the absence of an assumed application task, AM confronted the issue of determining what to learn. It exploited an extensive set of heuristics that estimated the interestingness of a new domain concept, learning only new ....

....the knowledge to ensure the response can be inexpensively computed for subsequent requests. However, performance failure is not the only catalyst for learning. AM, for example, uses heuristics to determine whether a new mathematical concept is interesting enough to add to its current knowledge [Len76] and Cobweb uses heuristics that assess the predictive power of new potential concepts to determine which concepts should be learned [Fis87] Additional examples will be presented in Chapters 3 and 5. 2.2.3 Discussion The REACT model decomposes the very general task of knowledge integration into ....

[Article contains additional citation context not shown here]

D.B. Lenat. AM: An artificial intelligence approach to discovery in mathematics as heuristic search. Technical report, Ph.D. dissertation, Computer Science Department, Stanford University, 1976.

....have implemented a system which automatically generates examples for a constraint stated in the theory and we have experimented with the system in the BoyerMoore theorem prover. 1.1 An Overview Examples are, in general, a very useful tool in Artificial Intelligence. Many machine learning systems [52, 33, 10, 14, 32] use examples for the tasks of generating concepts and conjectures. For instance, Winston s system [52] learns structural descriptions from examples. His system is presented with training instances positive examples and near misses of a structure (concept) to be learned such as an arch and ....

....and it is converted by the system into a semantic network representation. Such representations of training instances are used to modify the current representation of the concept in such a way that the new representation accepts the positive examples but rejects the near misses. Lenat s AM [33] automatically discovers concepts and conjectures in number theory from some concepts of elementary set theory. Discovery in AM is guided by heuristic rules; examples play an important role in AM. Being guided by some of the heuristic rules, examples are generated when a new concept is generated ....

[Article contains additional citation context not shown here]

Lenat, D. B. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. Ph.D. Th., Stanford University, 1976.

....help of an external cue. KDSA ID , by contrast, is designed to retrieve semantically distant analogies without necessarily being aided by an external cue. Another approach to computational creativity that, like KDSA ID , uses heuristics to evaluate the interestingness of a concept is Lenat s AM [Lenat, 1976]. However, KDSA ID differs from AM in the way that new concepts are generated: AM created entirely new concepts by modifying slots in existing ones, while KDSA ID retrieves concepts that are already in its knowledge base. Another body of related research lies in the collection of approaches to ....

D. B. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD thesis, Stanford University, 1976.

....concepts and discuss how this has led to the introduction of new mathematics. We also show how a theory can be constructed from just the axioms of an algebra, and how the heuristic search improves the overall quality of the theory with respect to various measures. 1. 1 Background Lenat, in [ Lenat, 1976 ] chose pure mathematics as the domain for his AM program to demonstrate the use of heuristic search in concept formation. AM re invented classically interesting definitions and conjectures, such as highly composite numbers and Goldbach s conjecture. The conjectures were based on empirical ....

D Lenat. AM: An artificial intelligence approach to discovery in mathematics. PhD thesis, Stanford University, 1976.

....specification of intermediate state, causal constraints, and argument structure and heuristics. Second, models of scientific discovery need to incorporate everyday layperson techniques of reasoning and creativity. What is the potential benefit of taking such an approach Over a decade ago, Lenat (1982) reported on AM, a model of discovery which used heuristics of interestingness as a focusing technique in the analysis of data. We claim that additional focusing techniques, such as those provided by prior knowledge play a major role in discovery in the intuitive scientist and the practicing ....

Lenat, D. (1982). AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. In Knowledge-based Systems in Artificial Intelligence. Edited by R. Davis and D.B. Lenat. New York: McGraw-Hill.

....Step 2. Identify Plausible Operations RIAM, similarly to AM, will use heuristics to identify plausible operations. A heuristic will be an antecedent consequent pair and will be applied by testing the antecedent a lisp predicate with no side effects except for the matching of variables (c.f. Lenat [1977])and if the antecedent evaluates to TRUE, performing the consequent, having one or more effects: 1. The identification of an operation and its placement onto the agenda, along with the creation of reasons for performing the operation and ratings for those reasons. If the operation is already on ....

....the operations in descending order by their plausibility and then remove and execute the operation with the greatest plausibility from the agenda. An operation s plausibility 2 will represent RIAM s estimation of the operation s potential for leading the process to interesting discoveries (c.f. Lenat [1977]) An operation O s plausibility will be calculated as a function of the ratings of the O s reasons and its operand s user interests and kdd worths: 3 priority O R cww W ciw I i j j ( 2 2 2 where R i is the rating of O s reason i, W j is the worth of O s operand j; I j is the ....

[Article contains additional citation context not shown here]

Lenat, D. B. (1977). "AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search." Computer Science Department, Stanford, CA, Stanford University.

....only attracted occasional SMC research level attention. It deserves much more. Typically, the generalisations that are the outputs of machine learning methods are generated and expressed in a logic based notation. An early example of such activity in a field highly relevant to SMC, the AM project [40], has been famous in its time, but also controversial [41] In general, AM style automated discovery of interesting terms, conjectures etc. in mathematics is a difficult job. As we have said above, certain difficulties (inefficiencies) in logic based computations can be reduced or removed if one ....

D.B. Lenat, AM: an Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search, in Knowledge-Based Systems in Artificial Intelligence, eds. R. Davis and D. Lenat, p. 3. McGraw-Hill, New York (1982)

....many cases, directly in terms of the list, i.e. the primitive data type of the LISP programming language. In addition, the lists in Lenat s artificial mathematician (AM) laws were manipulated by list manipulation functions that are unique or peculiar to LISP. Specifically, in many experiments in Lenat (1976), the mathematical laws sought were stated directly in terms of lists and list manipulation functions such as, CAR (which returns the first element of a list) CDR (which returns the tail of a list) etc. In Lenat s mea culpa article Why AM and EURISKO appear to work (Lenat and Brown 1984) ....

Lenat, Douglas B. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD Dissertation. Computer Science Department. Stanford University. 1976.

....unsupervised learning. However, systems that learn by discovery are more active in their search for new categories than systems learning by observation. They exploit their domain, sometimes by experiments, rather than passively observe it. The most famous system of this kind is Lenat s AM system (Lenat, 1976; Lenat, 1977) Another well known system is GLAUBER (Langley et al. 1983) AM works in the domain of mathematics and searches for and develops new interesting categories after being given a set of heuristic rules and basic concepts. It uses a generate and test strategy to form hypotheses on ....

Lenat, D. (1976). AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD thesis, Stanford University.

....their researchers or the outsiders. Furthermore, we seldom see insights obtained within an area transferred to a different one even though they are all aspects of intelligence as we know it. We have many systems that can be called intelligent in the sense that they produce interesting behavior [Lenat 82, Lenat and Brown 83] As Simon observed [Simon 69] complex behavior can arise from a simple mechanism within a complex environment. This seems to be the case when our AI programs produce interesting behavior. Other systems can be called intelligent because they give intelligent results. Expert ....

Lenat, D. B. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. In Davis, R. and Lenat, D. B. (editors), Knowledge-Based Systems in Artificial Intelligence. McGraw-Hill, New York, NY, 1982. 14

....period. 1 Introduction Despite the large number of efforts made for inventing efficient search algorithms for blackbox optimization problems, little systematic work has been done to explore the fundamental requirements for polynomial complexity search capability. The work on AM and EURISKO [9] pointed out the importance of the relative behavior of representation with respect to the search operators. Holland s work on genetic algorithms (GAs) initiated somewhat earlier burgeoned to Adaptation in Natural and Artificial Systems [6] almost at the same time. Holland s observation about the ....

D. B. Lenat. AM: An artificial intelligence approach to discovery in mathematics as heuristic search, Ph.D. Thesis, AIM-286, STAN-CS-76-570, Stanford, CA, 1976.

....concepts and discuss how this has led to the introduction of new mathematics. We also show how a theory can be constructed from just the axioms of an algebra, and how the heuristic search improves the overall quality of the theory with respect to various measures. 1. 1 Background Lenat, in [ Lenat, 1976 ] chose pure mathematics as the domain for his AM program to demonstrate the use of heuristic search in concept formation. AM re invented classically interesting definitions and conjectures, such as highly composite numbers and Goldbach s conjecture. The conjectures were based on empirical ....

D Lenat. AM: An artificial intelligence approach to discovery in mathematics. PhD thesis, Stanford University, 1976.

No context found.

D.B. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD thesis, Stanford University, 1976.

No context found.

D Lenat. AM: An artificial intelligence approach to discovery in mathematics. Unpublished PhD thesis, Stanford University, 1976.

No context found.

D. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics. PhD thesis, Stanford University, 1976. 5

No context found.

D.B. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics as Heuristic Search. PhD thesis, Stanford University, 1976.

No context found.

D. Lenat. AM: An Artificial Intelligence Approach to Discovery in Mathematics. PhD thesis, Stanford University, 1976. 5

No context found.

D Lenat. AM: An Artificial Intelligence approach to discovery in mathematics. PhD thesis, Stanford University, 1976.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC