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The Journal of Symbolic Logic, 2023
AbstractIn this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of ...
MARÍA MANZANO +4 more
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AbstractIn this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of ...
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Dependently Typed Records in Type Theory
Formal Aspects of Computing, 2002Abstract.The languagePebbleof Burstall and Lampson proposed dependent types as the underlying principle in a unified framework to explain facilities for programming in the large, such asmodulesandsignatures, as well as for programming in the small. This proposal soon extended to large scale formal proof development as well.
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Proceedings and Addresses of the American Philosophical Association, 1973
In this paper I advocate a reexamination of mathematical logic in the tradition of Principia Mathematica and the early writings of Russell ([PoM], [OD], [ML]), to ask in what form it should now be studied in order to preserve certain important contributions of Russell and in order to compare it with the somewhat different Fregean tradition. This should
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In this paper I advocate a reexamination of mathematical logic in the tradition of Principia Mathematica and the early writings of Russell ([PoM], [OD], [ML]), to ask in what form it should now be studied in order to preserve certain important contributions of Russell and in order to compare it with the somewhat different Fregean tradition. This should
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Embedding intuitionistic-type theory in negationless-type theory
Mathematical Notes of the Academy of Sciences of the USSR, 1986In ''A formal system of negationless arithmetic that is consistent with respect to Heyting arithmetic'' [Mat. Zametki 36, No.4, 583-592 (1984; Zbl 0576.03037)] the author shows that Heyting arithmetic is a conservative extension of \(HA^ N\)- a system of negationless arithmetic, under certain interpretation.
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Journal of Symbolic Logic, 1971
In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very convenient framework in which to search for a proof of a wff believed to be a theorem. Moreover, it has proved possible to formulate many refinements of resolution
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In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very convenient framework in which to search for a proof of a wff believed to be a theorem. Moreover, it has proved possible to formulate many refinements of resolution
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