Specification and Integration of Theorem Provers and Computer Algebra Systems

Bertoli, Piergiorgio; Calmet, Jacques; Giunchiglia, Fausto; Homann, Karsten

doi:10.3233/fi-1999-391203

“…By integrating theorem proving with computer algebra, we would be opening up a wealth of potentially interoperable algorithms that have to date remained largely unintegrated. To cite one such example, in [35], the authors have developed a framework for exchange of information between the Maple computer algebra system and the Isabelle interactive theorem prover. They show a simple problem involving the proof of an elementary polynomial identity that could be solved with the combined system, but in neither system alone (see Fig.…”

Section: Robust Computer Algebra and Integrated Theorem Provingmentioning

confidence: 99%

Robust Computer Algebra, Theorem Proving, and Oracle AI

Sarma¹,

Hay²

2017

Preprint

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In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.

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“…By integrating theorem proving with computer algebra, we would be opening up a wealth of potentially interoperable algorithms that have to date remained largely unintegrated. To cite one such example, in [34], the authors have developed a framework for exchange of information between the Maple computer algebra system and the Isabelle interactive theorem prover. They show a simple problem involving the proof of an elementary polynomial identity that could be solved with the combined system, but in neither system alone (see Fig.…”

Section: Iii3 Briefly Clarifying Nomenclaturementioning

confidence: 99%

Robust Computer Algebra, Theorem Proving, and Oracle AI

Sarma

¹

,

Hay

²

2017

SSRN Journal

2

0

View full text Add to dashboard Cite

In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.

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“…The problem of integrating deduction techniques into computer algebra has attracted considerable interest [24,10,3], and standard computer algebra systems (such as Mathematica [26]) already provides some equation simplification tools. Although they are powerful, no methods/techniques are available for designing a solver extension or to ensure its soundness.…”

Section: Motivationsmentioning

confidence: 99%

“…A partial solver is a computable function S satisfying only conditions (1) and (3). A non-deterministi c solver is S = (Sik=i, ... ,m such that…”

Section: Basic Conceptsmentioning

confidence: 99%

An Open Automated Framework for Constraint Solver Extension: the SoleX Approach

Monfroy

¹

,

Ringeissen

²

1999

Fundamenta Informaticae

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In declarative programming languages based on the constraint programming paradigm, computations can be viewed as deductions enhanced with the use of constraint solvers. However, admissible constraints are restricted to formulae handled by solvers and thus, declarativity may be jeopardized. We propose a domain-independent scheme to extend constraint solvers so that they can handle alien constraints, i.e., constraint involving new function symbols. This mechanism, called SoleX, consists of a set of symbolic rule-based transformations: they add and deduce syntactical as well as semantic information related to alien constraints, complete the computation domain, and purify constraints in order to allow solvers to cope with alien constraints. These transformations can be seen as elementary solvers, and thus, SoleX is a collaboration of these several solvers with the initial solver. Some extensions of computation domains have already been studied to demonstrate the broad scope of SoleX potential applications.

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Specification and Integration of Theorem Provers and Computer Algebra Systems

Cited by 10 publications

References 12 publications

Robust Computer Algebra, Theorem Proving, and Oracle AI

Robust Computer Algebra, Theorem Proving, and Oracle AI

Robust Computer Algebra, Theorem Proving, and Oracle AI

An Open Automated Framework for Constraint Solver Extension: the SoleX Approach

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