Results 1 to 10 of about 86 (68)
Interactive Learning-Based Realizability for Heyting Arithmetic with EM1 [PDF]
Logical Methods in Computer Science, 2010 We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for $\vee, \exists$) over ...
Federico Aschieri, Stefano Berardi
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An Interpretation of E-HA$^w$ inside HA$^w$
Electronic Proceedings in Theoretical Computer Science, 2023 Higher Type Arithmetic (HA$^w$) is a first-order many-sorted theory. It is a conservative extension of Heyting Arithmetic obtained by extending the syntax of terms to all of System T: the objects of interest here are the functionals of higher types ...
Castro, Félix
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Strong Normalization for HA + EM1 by Non-Deterministic Choice [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 We study the strong normalization of a new Curry-Howard correspondence for HA + EM1, constructive Heyting Arithmetic with the excluded middle on Sigma01-formulas.
Federico Aschieri
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Theoria, Volume 89, Issue 5, Page 660-670, October 2023., 2023 Abstract At the beginning of the twentieth century, among the foundational schools of mathematics appeared ‘intuitionism’ by Dutchman L. E. J. Brouwer, who based arithmetic on the intuition of time and all mental constructions that could be made out of it.
Miriam Franchella
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On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices
International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022 The concept of state has been considered in commutative and noncommutative logical systems, and their properties are at the center for the development of an algebraic investigation of probabilistic models for those algebras. This article mainly focuses on the study of the lattice of state ideals in De Morgan state residuated lattices (DMSRLs).
Francis Woumfo +4 more
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Proofs as stateful programs: A first-order logic with abstract Hoare triples, and an interpretation into an imperative language [PDF]
Logical Methods in Computer ScienceWe introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare logic, and the ...
Thomas Powell
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Connectedness of the continuum in intuitionistic mathematics
Mathematical Logic Quarterly, Volume 64, Issue 4-5, Page 387-394, November 2018., 2018 Abstract Working in (Intuitionistic analysis) we prove a strong, constructive connectedness property of the continuum: for any non‐empty sets, A and B, if then is non‐empty. It is well known that the intuitionistic continuum is indecomposable: if and then or , but this property is essentially negative—equivalent to if A, B are non‐empty and then .
Mark Bickford
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Philosophia ScientiæPoincaré’s position is often presented as semi-intuitionist, especially in relation to his position in arithmetic. This article examines Poincaré’s relationship to an intuitionist position.
Gerhard Heinzmann
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Where Mathematical Symbols Come From
Topics in Cognitive Science, Volume 18, Issue 1, Page 169-186, January 2026.Abstract There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ‘+$+$’ or ‘8’ by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice.
Dirk Schlimm
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Prawitz's completeness conjecture: A reassessment
Theoria, Volume 90, Issue 5, Page 492-514, October 2024.Abstract In 1973, Dag Prawitz conjectured that the calculus of intuitionistic logic is complete with respect to his notion of validity of arguments. On the background of the recent disproof of this conjecture by Piecha, de Campos Sanz and Schroeder‐Heister, we discuss possible strategies of saving Prawitz's intentions.
Peter Schroeder‐Heister
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