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Logic%2c Sets And Functions by Daniel A. Bonevac

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1Sets, Functions, And Logic : An Introduction To Abstract Mathematics

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  • Title: ➤  Sets, Functions, And Logic : An Introduction To Abstract Mathematics
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The book is available for download in "texts" format, the size of the file-s is: 439.82 Mbs, the file-s for this book were downloaded 435 times, the file-s went public at Wed Aug 14 2019.

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2From Nominal Sets Binding To Functions And Lambda-abstraction: Connecting The Logic Of Permutation Models With The Logic Of Functions

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Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just term-formers satisfying axioms, and their denotation is functions on nominal atoms-abstraction. Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo-Fraenkel) sets; the denotation of forall or lambda is functions on full or partial function spaces. This raises the following question: how are these two models of binding connected? What translation is possible between PNL and HOL, and between nominal sets and functions? We exhibit a translation of PNL into HOL, and from models of PNL to certain models of HOL. It is natural, but also partial: we translate a restricted subsystem of full PNL to HOL. The extra part which does not translate is the symmetry properties of nominal sets with respect to permutations. To use a little nominal jargon: we can translate names and binding, but not their nominal equivariance properties. This seems reasonable since HOL---and ordinary sets---are not equivariant. Thus viewed through this translation, PNL and HOL and their models do different things, but they enjoy non-trivial and rich subsystems which are isomorphic.

“From Nominal Sets Binding To Functions And Lambda-abstraction: Connecting The Logic Of Permutation Models With The Logic Of Functions” Metadata:

  • Title: ➤  From Nominal Sets Binding To Functions And Lambda-abstraction: Connecting The Logic Of Permutation Models With The Logic Of Functions
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 20.00 Mbs, the file-s for this book were downloaded 89 times, the file-s went public at Mon Sep 23 2013.

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3DTIC AD0758651: Axioms And Theorems For Integers, Lists And Finite Sets In Logic For Computable Functions (LCF)

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LCF (Logic for Computable Functions) is being promoted as a formal language suitable for the discussion of various problems in the Mathematical Theory of Computation (MTC). To this end, several examples of MTC problems have been formalised and proofs have been exhibited using the LCF proof-checker. However, in these examples, there has been a certain amount of ad-hoc-ery in the proofs: namely, many mathematical theorems have been assumed without proof and no axiomatisation of the mathematical domains involved was given. The paper describes a suitable mathematical environment for future LCF experiments and its axiomatic basis. The environment developed, deemed appropriate for such experiments, consists of a large body of theorems from the areas of integer arithmetic, list manipulation and finite set theory.

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  • Title: ➤  DTIC AD0758651: Axioms And Theorems For Integers, Lists And Finite Sets In Logic For Computable Functions (LCF)
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 34.12 Mbs, the file-s for this book were downloaded 80 times, the file-s went public at Sun May 19 2019.

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4Sets, Functions And Logic- An Introduction To Abstract Mathematics, Keith Devlin, Chapman And Hall, 1992

Sets, functions and logic- an introduction to abstract mathematics, Keith Devlin, Chapman and Hall, 1992

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  • Title: ➤  Sets, Functions And Logic- An Introduction To Abstract Mathematics, Keith Devlin, Chapman And Hall, 1992

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