13 found
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  1.  3
    De Zolt’s Postulate: An Abstract Approach.Eduardo N. Giovannini, Edward H. Haeusler, Abel Lassalle-Casanave & Paulo A. S. Veloso - forthcoming - Review of Symbolic Logic:1-28.
    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.  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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  3.  14
    De la Práctica Euclidiana a la Práctica Hilbertiana: Las Teorías Del Área Plana.Eduardo N. Giovannini, Abel Lassalle Casanave & Paulo A. S. Veloso - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1263-1294.
    This paper analyzes the theory of area developed by Euclid in the Elements and its modern reinterpretation in Hilbert’s influential monograph Foundations of Geometry. Particular attention is bestowed upon the role that two specific principles play in these theories, namely the famous common notion 5 and the geometrical proposition known as De Zolt’s postulate. On the one hand, we argue that an adequate elucidation of how these two principles are conceptually related in the theories of Euclid and Hilbert is highly (...)
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  4.  34
    On Ultrafilter Logic and Special Functions.Paulo A. S. Veloso & Sheila R. M. Veloso - 2004 - Studia Logica 78 (3):459-477.
    Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.
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  5.  11
    On Modulated Logics for 'Generally' : Some Metamathematical Issues.Sheila R. M. Veloso & Paulo A. S. Veloso - unknown
  6.  92
    On What There Must Be: Existence in Logic and Some Related Riddles.Paulo A. S. Veloso, Luiz Carlos Pereira & E. Hermann Haeusler - 2012 - Disputatio 4 (34):889-910.
    Veloso-Pereira-Haeusler_On-what-there-must-be.
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  7.  29
    Squares in Fork Arrow Logic.Renata P. de Freitas, Jorge P. Viana, Mario R. F. Benevides, Sheila R. M. Veloso & Paulo A. S. Veloso - 2003 - Journal of Philosophical Logic 32 (4):343-355.
    In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...)
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  8.  22
    Squares in Fork Arrow Logic.Renata P. De Freitas, Jorge P. Viana, Mario R. F. Benevides, Sheila R. M. Veloso & Paulo A. S. Veloso - 2003 - Journal of Philosophical Logic 32 (4):343 - 355.
    In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...)
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  9.  26
    On Fork Arrow Logic and its Expressive Power.Paulo A. S. Veloso, Renata P. de Freitas, Petrucio Viana, Mario Benevides & Sheila R. M. Veloso - 2007 - Journal of Philosophical Logic 36 (5):489 - 509.
    We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...)
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  10.  15
    On Reasoning About 'Generally' and 'Rarely' with Filter-Like Family of Sets.Paulo A. S. Veloso, Jean-Yves Béziau & Alexandre Costa Leite - unknown
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  11.  13
    On Fork Arrow Logic and Its Expressive Power.Paulo A. S. Veloso, Renata P. De Freitas, Petrucio Viana, Mario Benevides & Sheila R. M. Veloso - 2007 - Journal of Philosophical Logic 36 (5):489 - 509.
    We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...)
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  12.  8
    Definition-Like Extensions by Sorts.Claudia Meré María & Paulo A. S. Veloso - 1995 - Logic Journal of the IGPL 3 (4):579-595.
  13.  15
    A New, Simpler Proof of the Modularisation Theorem for Logical Specifications.Paulo A. S. Veloso - 1993 - Logic Journal of the IGPL 1 (1):3-12.