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ECC, an Extended Calculus of Constructions
, 1989
"... We present a higherorder calculus ECC which can be seen as an extension of the calculus of constructions [CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics ..."
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Cited by 84 (4 self)
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We present a higherorder calculus ECC which can be seen as an extension of the calculus of constructions [CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice prooftheoretic properties. An !\GammaSet (realizability) model is described to show how the essential properties of the calculus can be captured settheoretically.
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 46 (18 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,
Set Theory for Verification: II  Induction and Recursion
 Journal of Automated Reasoning
, 2000
"... A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning. ..."
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Cited by 43 (21 self)
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A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning.
Fair Games and Full Completeness for Multiplicative Linear Logic without the MIXRule
, 1993
"... We introduce a new category of finite, fair games, and winning strategies, and use it to provide a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted as games, and proofs as winning strategies. This interpretation provides a categorical model of mll wh ..."
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Cited by 40 (4 self)
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We introduce a new category of finite, fair games, and winning strategies, and use it to provide a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted as games, and proofs as winning strategies. This interpretation provides a categorical model of mll which satisfies the property that every (historyfree, uniformly) winning strategy is the denotation of a unique cutfree proof net. Abramsky and Jagadeesan first proved a result of this kind and they refer to this property as full completeness. Our result differs from theirs in one important aspect: the mixrule, which is not part of Girard's Linear Logic, is invalidated in our model. We achieve this sharper characterization by considering fair games. A finite, fair game is specified by the following data: ffl moves which Player can play, ffl moves which Opponent can play, and ffl a collection of finite sequences of maximal (or terminal) positions of the game which are deemed to be fair. N...
A New Formulation of Tabled Resolution with Delay
 In Recent Advances in Artifiial Intelligence
, 1999
"... . Tabling has become important to logic programming in part because it opens new application areas, such as model checking, to logic programming techniques. However, the development of new extensions of tabled logic programming is becoming restricted by the formalisms that underly it. Formalisms ..."
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Cited by 15 (14 self)
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. Tabling has become important to logic programming in part because it opens new application areas, such as model checking, to logic programming techniques. However, the development of new extensions of tabled logic programming is becoming restricted by the formalisms that underly it. Formalisms for tabled evaluations, such as SLG [3], are generally developed with a view to a specific set of allowable operations that can be performed in an evaluation. In the case of SLG, tabling operations are based on a variance relation between atoms. While the set of SLG tabling operations has proven useful for a number of applications, other types of operations, such as those based on a subsumption relation between atoms, can have practical uses. In this paper, SLG is reformulated in two ways: so that it can be parameterized using different sets of operations; and so that a forest of trees paradigm is used. Equivalence to SLG of the new formulation, Extended SLG or SLGX , is shown whe...
Isabelle’s isabelle’s logics: FOL and ZF
, 2003
"... This manual describes Isabelle’s formalizations of manysorted firstorder logic (FOL) and ZermeloFraenkel set theory (ZF). See the Reference Manual for general Isabelle commands, and Introduction to Isabelle for an overall tutorial. This manual is part of the earlier Isabelle documentation, which ..."
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Cited by 4 (3 self)
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This manual describes Isabelle’s formalizations of manysorted firstorder logic (FOL) and ZermeloFraenkel set theory (ZF). See the Reference Manual for general Isabelle commands, and Introduction to Isabelle for an overall tutorial. This manual is part of the earlier Isabelle documentation, which is somewhat superseded by the Isabelle/HOL Tutorial [11]. However, the present document is the only available documentation for Isabelle’s versions of firstorder
Cultural Heterogeneity and the Stability of Groups with Imperfect Information Transmission
, 1997
"... This paper seeks to extend current research into group stability by looking at the impact of information on the social structure of group members. As the primary vehicle for this examination, this paper will use Carley's CONSTRUCT model (1990a, 1990b, 1991) of group behavior as the theoretical frame ..."
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This paper seeks to extend current research into group stability by looking at the impact of information on the social structure of group members. As the primary vehicle for this examination, this paper will use Carley's CONSTRUCT model (1990a, 1990b, 1991) of group behavior as the theoretical framework. CONSTRUCT is a model of group behavior based on knowledgebased interaction. It is built around the assumption of homophilly  that group members with greater common knowledge tend to interact more often. Additionally, it incorporates social elements of information exchange and tightly links social structure with cognitive structure. Carley tests the model on Kapferer's (1972; Borgatti, Everett, and Freeman, 1992) African factory data and achieves accurate predictions in such a manner that allow her to conclude (1990a) that CONSTRUCT "closes the loop between individual and social change." Carley's work makes a useful basis from which to proceed largely because she achieves such accurate predictions at the group level from only the most primitive assumptions about individual behavior. Her sparse characterization of individuals, reminiscent of simple automata, allows the precise testing of specific behavioral assumptions and their direct consequences at the group level. The two most critical and most interesting assumptions are those of homophilly and communication. These two assumptions are closely linked and straightforward. Research has often shown that interaction among individuals is a function of various degrees of "commonality" among those individuals. As one might imagine, there are many ways to measure commonality and equally many ways to see why homophilly is so pervasive. Festinger (1954), for example, concludes that there are powerful innate forces compellin...
α Isabelle’s Logics: FOL and ZF
"... This manual describes Isabelle’s formalizations of manysorted firstorder logic (FOL) and ZermeloFraenkel set theory (ZF). See the Reference Manual for general Isabelle commands, and Introduction to Isabelle for an overall tutorial. This manual is part of the earlier Isabelle documentation, which ..."
Abstract
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This manual describes Isabelle’s formalizations of manysorted firstorder logic (FOL) and ZermeloFraenkel set theory (ZF). See the Reference Manual for general Isabelle commands, and Introduction to Isabelle for an overall tutorial. This manual is part of the earlier Isabelle documentation, which is somewhat superseded by the Isabelle/HOL Tutorial [11]. However, the present document is the only available documentation for Isabelle’s versions of firstorder