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Efficient Reasoning
 Computing Surveys
, 1998
"... Many tasks require "reasoning"  i.e., deriving conclusions from a corpus of explicitly stored information  to solve their range of problems. An ideal reasoning system would produce alland only the correct answers to every possible query, produce answers that are as specific as possible, be ex ..."
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Cited by 5 (1 self)
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Many tasks require "reasoning"  i.e., deriving conclusions from a corpus of explicitly stored information  to solve their range of problems. An ideal reasoning system would produce alland only the correct answers to every possible query, produce answers that are as specific as possible, be expressive enough to permit any possible fact to be stored and any possible query to be asked, and be efficient. Unfortunately, this is provably impossible: as correct and precise systems become more expressive, they become increasingly inefficient, or even undecidable. This tutorial first formalizes these hardness results, in the context of both logic and probabilitybased reasoning, then overviews the existing techniques now used to address, or at least sidestep, this dilemma. Throughout, we also include some alternative proposals. 1 Introduction Many information systems use a corpus of explicitly stored information (a.k.a. a "knowledge base", KB) to solve their range of problems. For exa...
OpenTheory: Package Management for Higher Order Logic Theories
"... Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective pack ..."
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Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective package management system for logical theories. The OpenTheory article format allows higher order logic theories to be exported from one theorem prover, compressed by a standalone tool, and imported into a different theorem prover. Articles naturally support theory interpretations, which is the mechanism by which theories can be cleanly transferred from one theorem prover context to another, and which also leads to more efficient developments of standard theories.
Formalizing abstract algebra in constructive set theory
, 2002
"... Abstract. We present a machinechecked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with ..."
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Abstract. We present a machinechecked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties of groups constructively from these inference rules as well as the axioms of the set theory. The formalization of all other concepts in abstract algebra is based on that of the group. We give an example of a formalization of a concrete group, the Klein 4group. 1
Superdeduction at Work
"... Abstract Superdeduction is a systematic way to extend a deduction system like the sequent calculus by new deduction rules computed from the user theory. We show how this could be done in a systematic, correct and complete way. We prove in detail the strong normalization of a proof term language that ..."
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Abstract Superdeduction is a systematic way to extend a deduction system like the sequent calculus by new deduction rules computed from the user theory. We show how this could be done in a systematic, correct and complete way. We prove in detail the strong normalization of a proof term language that models appropriately superdeduction. We finaly examplify on several examples, including equality and noetherian induction, the usefulness of this approach which is implemented in the lemuridæ system, written in TOM. 1