Some Aspects of Analogy in Mathematical Reasoning

An important research problem is the incorporation of “declarative” knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting proposal in this direction is Alan Bundy’s approach of using explicit proof plans that encapsulate the general form of a proof and is instantiated into a particular proof for the case at hand. We give some examples that show how a “declarative” highlevel description of a proof can be used to find proofs of apparently “similiar” theorems by analogy. This “analogical” information is used to select the appropriate axioms from the database so that the theorem can be proved. This information is also used to adjust some options of a resolution theorem prover. In order to get a powerful tool it is necessary to develop an epistemologically appropriate language to describe proofs, for which a large set of examples should be used as a testbed. We present some ideas in this direction

Approaches to the reuse of plan schemata in planning formalisms

Planning in complex domains is normally a resource and time consuming process when it is purely based on first principles. Once a plan is generated it represents problem solving knowledge. It implicitly describes knowledge used by the planning system to achieve a given goal state from a particular initial state. In classical planning systems, this knowledge is often lost after the plan has been successfully executed. If such a planner has to solve the same problem again, it will spend the same planning effort to solve it and is not capable of "learning\u27; from its "experience\u27;. Therefore it seems to be useful to save generated plans for a later reuse and thus, extending the problem solving knowledge possessed by the planner. The planning knowledge can now be applied to find out whether a problem can be solved by adapting an already existing plan. The aim of this paper is to analyze the problem of plan reuse and to describe the state of the art based on a variety of approaches which might contribute to a solution of the problem. It describes the main problems and results that could be of some relevance for the integration of plan reuse into a deductive planning formalism. As a result, this description of the state of the art leads to a deeper insight into the complex problem of plan reuse, but also shows that the problem itself is still far from being solved

Some Aspects of Analogy in Mathematical Reasoning

An important research problem is the incorporation of "declarative" knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting proposal in this direction is Alan Bundy's approach of using explicit proof plans that encapsulate the general form of a proof and is instantiated into a particular proof for the case at hand. We give some examples that show how a "declarative" highlevel description of a proof can be used to find proofs of apparently "similiar" theorems by analogy. This "analogical" information is used to select the appropriate axioms from the database so that the theorem can be proved. This information is also used to adjust some options of a resolution theorem prover. In order to get a powerful tool it is necessary to develop an epistemologically appropriate language to describe proofs, for which a large set of examples should be used as a testbed. We present some ideas in this direction. Keywords: analogy, theorem proving, proof..

Some Aspects of Analogy in Mathematical Reasoning

An important research problem is the incorporation of "declarative" knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting pro-posal in this direction is Alan Bundy's approach of using explicit proof plans that encapsulatethe general form of a proof and is instantiated into a particular proof for the case at hand. Wegive some examples that show how a "declarative" highlevel description of a proof can be usedto find proofs of apparently "similiar" theorems by analogy. This "analogical" information isused to select the appropriate axioms from the database so that the theorem can be proved.This information is also used to adjust some options of a resolution theorem prover. In orderto get a powerful tool it is necessary to develop an epistemologically appropriate language todescribe proofs, for which a large set of examples should be used as a testbed. We presentsome ideas in this direction

Some Aspects of Analogy in Mathematical Reasoning

An important research problem is the incorporation of "declarative" knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting pro-posal in this direction is Alan Bundy's approach of using explicit proof plans that encapsulatethe general form of a proof and is instantiated into a particular proof for the case at hand. Wegive some examples that show how a "declarative" highlevel description of a proof can be usedto find proofs of apparently "similiar" theorems by analogy. This "analogical" information isused to select the appropriate axioms from the database so that the theorem can be proved.This information is also used to adjust some options of a resolution theorem prover. In orderto get a powerful tool it is necessary to develop an epistemologically appropriate language todescribe proofs, for which a large set of examples should be used as a testbed. We presentsome ideas in this direction