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An Overview of Cooperative Answering
, 1992
"... Databases and information systems are often hard to use because they do not explicitly attempt to cooperate with their users. Direct answers to database and knowledge base queries may not always be the best answers. Instead, an answer with extra or alternative information may be more useful and less ..."
Abstract

Cited by 91 (10 self)
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Databases and information systems are often hard to use because they do not explicitly attempt to cooperate with their users. Direct answers to database and knowledge base queries may not always be the best answers. Instead, an answer with extra or alternative information may be more useful and less misleading to a user. This paper surveys foundational work that has been done toward endowing intelligent information systems with the ability to exhibit cooperative behavior. Grice's maxims of cooperative conversation, which provided a starting point for the field of cooperative answering, are presented along with relevant work in natural language dialogue systems, database query answering systems, and logic programming and deductive databases. The paper gives a detailed account of cooperative techniques that have been developed for considering users' beliefs and expecations, presuppositions, and misconceptions. Also, work in intensional answering and generalizing queries and answers is co...
Set theory for verification: I. From foundations to functions
 J. Auto. Reas
, 1993
"... A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherord ..."
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Cited by 45 (17 self)
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A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherorder syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor’s Theorem, the Composition of Homomorphisms challenge [9], and Ramsey’s Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics. Key words. Isabelle, set theory, generic theorem proving, Ramsey’s Theorem,
Formalized mathematics
 TURKU CENTRE FOR COMPUTER SCIENCE
, 1996
"... It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In c ..."
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Cited by 24 (0 self)
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It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In contrast to the QED Manifesto however, we do not offer polemics in support of such a project. We merely try to place the formalization of mathematics in its historical perspective, as well as looking at existing praxis and identifying what we regard as the most interesting issues, theoretical and practical.
Experiments with ZF Set Theory in HOL and Isabelle
 IN PROCEEDINGS OF THE 8TH INTERNATIONAL WORKSHOP ON HIGHER ORDER LOGIC THEOREM PROVING AND ITS APPLICATIONS, LNCS
, 1995
"... Most general purpose proof assistants support versions of typed higher order logic. Experience has shown that these logics are capable of representing most of the mathematical models needed in Computer Science. However, perhaps there exist applications where ZFstyle set theory is more natural, ..."
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Cited by 13 (1 self)
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Most general purpose proof assistants support versions of typed higher order logic. Experience has shown that these logics are capable of representing most of the mathematical models needed in Computer Science. However, perhaps there exist applications where ZFstyle set theory is more natural, or even necessary. Examples may include Scott's classical inverselimit construction of a model of the untyped  calculus (D1 ) and the semantics of parts of the Z specification notation. This paper
Merging HOL with Set Theory  preliminary experiments
, 1994
"... Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory w ..."
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Cited by 11 (1 self)
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Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory works well and provides, for specification, the benefits of typechecking that are wellknown in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, whereas type theory may appear inaccessable and so be an obstacle to the uptake of proof assistants based on it. This paper describes some experiments (using HOL) in combining set theory and type theory; the aim is to get the best of both worlds in a single system. Three approaches have been tried, all based on an axiomatically specified type V of ZFlike sets: (i) HOL is used without any additions besides V; (ii) an emb...
Set Theory, Higher Order Logic or Both?
"... The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are ..."
Abstract

Cited by 7 (0 self)
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The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are wellknown in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, but not higher order logic. This paper discusses some approaches to getting the best of both worlds: the expressiveness and standardness of set theory with the efficient treatment of functions provided by typed higher order logic.
An Overview of Cooperative Answering
, 1992
"... Databases and information systems are often hard to use because they do not explicitly attempt to cooperate with their users. Direct answers to database and knowledge base queries may not always be the best answers. Instead, an answer with extra or alternative information may be more useful and less ..."
Abstract

Cited by 1 (0 self)
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Databases and information systems are often hard to use because they do not explicitly attempt to cooperate with their users. Direct answers to database and knowledge base queries may not always be the best answers. Instead, an answer with extra or alternative information may be more useful and less misleading to a user. This paper surveys foundational work that has been done toward endowing intelligent information systems with the ability to exhibit cooperative behavior. Grice's maxims of cooperative conversation, which provided a starting point for the field of cooperative answering, are presented along with relevant work in natural language dialogue systems, database query answering systems, and logic programming and deductive databases. The paper gives a detailed account of cooperative techniques that have been developed for considering users' beliefs and expecations, presuppositions, and misconceptions. Also, work in intensional answering and generalizing queries and answers is c...