16 found
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Edward Hermann Haeusler [13]Edward H. Haeusler [4]
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Edward Haeusler
Pontifícia Universidade Católica do Rio de Janeiro
  1.  7
    De Zolt’s Postulate: An Abstract Approach.Eduardo N. Giovannini, Edward H. Haeusler, Abel Lassalle-Casanave & Paulo A. S. Veloso - 2022 - Review of Symbolic Logic 15 (1):197-224.
    A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons. We formulate an abstract version of this postulate and derive it from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5, and analyze its logical relation to the former proposition. These results prove (...)
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  2.  18
    Proof Compression and NP Versus PSPACE II.Lew Gordeev & Edward Hermann Haeusler - 2020 - Bulletin of the Section of Logic 49 (3):213-230.
    We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal propositional logic is known to be PSPACE complete, while PSPACE to include NP, it suffices to show that every valid purely implicational formula ρ has a proof whose weight and time complexity of the provability involved are both polynomial in the weight of (...)
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  3.  28
    A New Normalization Strategy for the Implicational Fragment of Classical Propositional Logic.Luiz C. Pereira, Edward H. Haeusler, Vaston G. Costa & Wagner Sanz - 2010 - Studia Logica 96 (1):95-108.
    The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...)
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  4.  31
    Validades Existenciais e Enigmas Relacionados.Paulo A. S. Veloso, Luiz Carlos Pereira & Edward H. Haeusler - 2009 - Dois Pontos 6 (2).
    Logic does not have purely existential theorems: the only existential sentences that are valid are those with valid universal analogues. Here, we show indeed this is so, when properly interpreted: every existential validity has a simple universal analogue, which is also valid. We also characterize existential and universal validities in terms of tautologies.
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  5.  16
    NUL-Natural Deduction for Ultrafilter Logic.Christian Jacques Renterıa, Edward Hermann Haeusler & Paulo As Veloso - 2003 - Bulletin of the Section of Logic 32 (4):191-199.
  6. The Rules-as-Types Interpretation of Schroder-Heister's Extension of Natural Deduction.Edward Hermann Haeusler & Luiz Carlos Pd Pereira - 1999 - Manuscrito 22 (2):149.
     
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  7.  2
    Advances in Natural Deduction: A Celebration of Dag Prawitz's Work.Luiz Carlos Pereira & Edward Hermann Haeusler (eds.) - 2012 - Dordrecht, Netherland: Springer.
    This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...)
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  8.  34
    A Formalization of Sambins's Normalization for GL.Edward Hermann Haeusler & Luiz Carlos Pereira - 1993 - Mathematical Logic Quarterly 39 (1):133-142.
    Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically (...)
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  9.  31
    An Infinitary Extension of Mall−.Luiz Carlos Pd Pereira & Edward Hermann Haeusler - 1999 - Bulletin of the Section of Logic 28 (4):225-233.
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  10. Sí­ntese Construtiva de Programas Utilizando Lógica Institucionista e Dedução Natural.Geiza Maria Hamazaki da Silva & Edward Hermann Haeusler - 2001 - Princípios 8 (10):25-61.
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  11.  23
    Some Models of Heterogeneous and Distributed Specifications Based on Universal Constructions.Edward Hermann Haeusler, Alfio Martini & Uwe Wolter - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic.
  12.  1
    Proof Compression and NP Versus PSPACE II: Addendum.Lew Gordeev & Edward Hermann Haeusler - 2022 - Bulletin of the Section of Logic 51 (2):197-205.
    In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, (...)
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  13.  21
    Completeness of an Action Logic for Timed Transition Systems.Fernando Náufel do Amaral & Edward Hermann Haeusler - 2000 - Bulletin of the Section of Logic 29 (4):151-160.
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  14.  21
    XII Brazilian Logic Conference.Edward Hermann Haeusler - 2001 - Bulletin of Symbolic Logic 7 (2):295-295.
  15.  18
    A Natural Deduction System for Ctl.Christian Jacques Renterıa & Edward Hermann Haeusler - 2002 - Bulletin of the Section of Logic 31 (4):231-240.
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  16.  14
    A Concrete Categorical Model for the Lambek Syntactic Calculus.Marcelo Da Silva Corrêa & Edward Hermann Haeusler - 1997 - Mathematical Logic Quarterly 43 (1):49-59.
    We present a categorical/denotational semantics for the Lambek Syntactic Calculus , indeed for a λlD-typed version Curry-Howard isomorphic to it. The main novelty of our approach is an abstract noncommutative construction with right and left adjoints, called sequential product. It is defined through a hierarchical structure of categories reflecting the implicit permission to sequence expressions and the inductive construction of compound expressions. We claim that Lambek's noncommutative product corresponds to a noncommutative bi-endofunctor into a category, which encloses all categories of (...)
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