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ON THE REDUCTION OF TYPE THEORY
Mathematical Logic Quarterly, 1983The paper concerns a theorem of Grishin, who showed that New Foundations and type theory are reducible to a system of axioms containing only four consecutive types. On the other hand, M. Boffa showed, that this is the best possible result because the reduction to three consecutive types is impossible.
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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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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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ACM SIGPLAN Notices, 1982
A mathematical model for the notion "data type" is presented. The proposed theory seems to be at least as powerful as the initial algebra approach (see [1]), but can be handled far more easily. A clear distinction is drawn between algebras that are data types and those being merely implementations of types.
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A mathematical model for the notion "data type" is presented. The proposed theory seems to be at least as powerful as the initial algebra approach (see [1]), but can be handled far more easily. A clear distinction is drawn between algebras that are data types and those being merely implementations of types.
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Fuzzy Sets and Systems, 2005
Fuzzy logic was originally invented to describe human reasoning. The original fuzzy logic covered only propositional formulas. Later, quantifiers were added to fuzzy logic. However, an important part of human reasoning is still missing from fuzzy logic: arguments that usually require a higher-order logic. For example, we can say that \(X\) is a typical
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Fuzzy logic was originally invented to describe human reasoning. The original fuzzy logic covered only propositional formulas. Later, quantifiers were added to fuzzy logic. However, an important part of human reasoning is still missing from fuzzy logic: arguments that usually require a higher-order logic. For example, we can say that \(X\) is a typical
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Arithmetic and the theory of types
Journal of Symbolic Logic, 1984A hundred years ago, Frege proposed a logical definition of the natural numbers based on the following idea:He replaced this circular definition by the following one:He tried afterwards to found his theory over a notion of class satisfying a general comprehension principle:Russell quickly derived a contradiction from this principle (the famous Russell ...
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1996
We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory.
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We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory.
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Abstract Data Types and Type Theory: Theories as Types
Mathematical Logic Quarterly, 1991Ruy J. G. B. de Queiroz +1 more
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Completeness in the theory of types
Journal of Symbolic Logic, 1950The first order functional calculus was proved complete by Gödel in 1930. Roughly speaking, this proof demonstrates that each formula of the calculus is a formal theorem which becomes a true sentence under every one of a certain intended class of interpretations of the formal system.For the functional calculus of second order, in which predicate ...
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Nuclear Effective Field Theory: Status and Perspectives
Reviews of Modern Physics, 2020Ubirajara van Kolck +2 more
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