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Paulo A. S. Veloso [13]Paulo Veloso [11]Paulo As Veloso [11]Paulo S. Veloso [3]
Paulo A. Veloso [1]
  1.  27
    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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  2.  11
    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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  3.  16
    On Vague Notions and Modalities: A Modular Approach.Paulo Veloso, Sheila Veloso, Petrúcio Viana, Renata de Freitas & Mario Benevides - 2010 - Logic Journal of the IGPL 18 (3):381-402.
    Vague notions, such as ‘generally’, ‘rarely’, ‘often’, ‘almost always’, ‘a meaningful subset of a whole’, ‘most’, etc., occur often in ordinary language and in some branches of science. We introduce modal logical systems, with generalized operators, for the precise treatment of assertions involving some versions of such vague notions. We examine modal logics, constructed in a modular fashion, with generalized operators corresponding to some versions of ‘generally’ and ‘rarely’.
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  4.  8
    On a Logic for 'Almost All' and 'Generic' Reasoning.Paulo Veloso - 2002 - Manuscrito 25 (1):191-271.
    Some arguments use ‘generic’, or ‘typical’, objects. An explanation for this idea in terms of ‘almost all’ is suggested. The intuition of ‘almost all’ as ‘but for a few exceptions’ is rendered precise by means of ultrafilters. A logical system, with generalized quantifiers for ‘almost all’, is proposed as a basis for generic reasoning. This logic is monotonic, has a simple sound and complete deductive calculus, and is a conservative extension of classical first-order logic, with which it shares several properties. (...)
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  5.  15
    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.  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.  30
    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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  8.  13
    A Finitary Relational Algebra for Classical First-Order Logic.Paulo As Veloso & Armando M. Haeberer - 1991 - Bulletin of the Section of Logic 20 (2):52-62.
  9.  28
    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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  10.  24
    Characterisations for Fork Algebras and Their Relational Reducts.Paulo As Veloso - 1997 - Bulletin of the Section of Logic 26 (3):144-155.
  11.  4
    A New, Simpler Proof Of The Modularisation Theorem For Logical Specifications.Paulo S. Veloso - 1993 - Logic Journal of the IGPL 1 (1):3-12.
    A new, simpler proof, based on internalisation of interpretations, of the Modularisation Theorem for logical specifications is presented. This result is a basic tool for composing implementations and specialisation by parameter instantiation.
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  12.  13
    On the Power of Ultrafilter Logic.Paulo As Veloso - 2000 - Bulletin of the Section of Logic 29 (3):89-97.
  13.  4
    Functional Interpretation of Logics for ‘Generally’.Paulo Veloso & Sheila Veloso - 2004 - Logic Journal of the IGPL 12 (6):627-640.
    Logics for ‘generally’ are intended to express some vague notions, such as ‘generally’, ‘several’, ‘many’, ‘most’, etc., by means of the new generalized quantifier ∇ and to reason about assertions with ‘generally’ . We introduce the idea of functional interpretation for ‘generally’ and show that representative functions enable elimination of ∇ and reduce consequence to classical theories. Thus, one can use proof procedures and theorem provers for classical first-order logic to reason about assertions involving ‘generally’.
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  14.  1
    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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  15.  7
    A Finite Axiomatization For Fork Algebras.Marcelo Frias, Armando Haeberer & Paulo S. Veloso - 1997 - Logic Journal of the IGPL 5 (3):1-10.
    Proper fork algebras are algebras of binary relations over a structured set. The underlying set has changed from a set of pairs to a set closed under an injective function. In this paper we present a representation theorem for their abstract counterpart, that entails that proper fork algebras — whose underlying set is closed under an injective function — constitute a finitely based variety.1.
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  16.  24
    On ‘Most’ and ‘Representative’: Filter Logic and Special Predicates.Paulo Veloso & Sheila Veloso - 2005 - Logic Journal of the IGPL 13 (6):717-728.
    Logics for ‘generally’ were introduced for handling assertions with vague notions, by non-standard generalized quantifiers, and to reason qualitatively about them . Filter logic is intended to address ‘most’. Here, we show that filter logic can be faithfully embedded into a classical first-order theory of certain predicates, called compatible. We also use representative predicates to enable elimination of the generalized quantifier. These devices permit using classical first-order methods to reason about consequence in filter logic and help clarifying the role of (...)
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  17. A Logical Approach To Qualitative Reasoning With 'Several'.Paulo Veloso - 2001 - Logique Et Analyse 44.
     
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  18.  20
    Why Ultrafilters for Almost All.Paulo As Veloso - 1999 - Bulletin of the Section of Logic 28 (4):183-193.
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  19.  18
    Is Fork Set-Theoretical.Paulo As Veloso - 1997 - Bulletin of the Section of Logic 26 (1):20-30.
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  20.  16
    On Some Misconceptions About Ultrafilter Logic.Paulo As Veloso - 2000 - Bulletin of the Section of Logic 29 (1/2):1-12.
  21.  16
    On the Independence of the Axioms for Fork Algebras.Paulo As Veloso - 1997 - Bulletin of the Section of Logic 26 (4):197-209.
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  22.  18
    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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  23.  23
    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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  24.  9
    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.
  25.  8
    Definition-Like Extensions by Sorts.Claudia Meré María & Paulo A. S. Veloso - 1995 - Logic Journal of the IGPL 3 (4):579-595.
  26.  14
    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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  27.  11
    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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  28.  8
    Exploring Computational Contents of Intuitionist Proofs.Geiza Hamazaki da Silva, Edward Haeusler & Paulo Veloso - 2005 - Logic Journal of the IGPL 13 (1):69-93.
    One of the main problems in computer science is to ensure that programs are implemented in such a way that they satisfy a given specification. There are many studies about methods to prove correctness of programs. This work presents a method, belonging to the constructive synthesis or proofs-as-programs paradigm, that comes from the Curry-Howard isomorphism and extracts the computational contents of intuitionist proofs. The synthesis process proposed produces a program in an imperative language from a proof in many-sorted intuitionist logic, (...)
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  29.  10
    On Modulated Logics for 'Generally' : Some Metamathematical Issues.Sheila R. M. Veloso & Paulo A. S. Veloso - unknown
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  30.  8
    On Eight Independent Equational Axiomatisations for Fork Algebras.Paulo As Veloso - 1998 - Bulletin of the Section of Logic 27 (3):117-129.
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  31.  7
    An Application of Logic Engineering.Sheila Veloso, Paulo Veloso & Renata de Freitas - 2005 - Logic Journal of the IGPL 13 (1):29-46.
    We consider a paradigm of applications of Logic Engineering to illustrate the information interchange among different areas of knowledge, through the formal approach to some aspects of computing. We apply the paradigm to the area of distributed systems, taking the demand for specification formalisms, treated in three areas of knowledge: modal logics, first-order logic and algebra. In doing so, we obtain transfer of intuitions and results, establishing that, as far as input/output representation is concerned, these three formalisms are equivalent.
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  32.  5
    On Positive Relational Calculi.Renata de Freitas, Paulo Veloso, Sheila Veloso & Petrucio Viana - 2007 - Logic Journal of the IGPL 15 (5-6):577-601.
    We discuss the question of inclusions between positive relational terms and some of its aspects, using the form of a dialogue. Two possible approaches to the problem are emphasized: natural deduction and graph manipulations. Both provide sound and complete calculi for proving the valid inclusions, supporting nice strategies to obtain proofs in normal form, but the latter appears to present several advantages, which are discussed.
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  33.  4
    Natural Deduction for ‘Generally’.Leonardo Vana, Paulo Veloso & Sheila Veloso - 2007 - Logic Journal of the IGPL 15 (5-6):775-800.
    Logics for ‘generally’ were introduced for handling assertions with vague notions , which occur often in ordinary language and in science. LG’s provide a framework for distinct notions of ‘generally’: one builds a specific logic for the notion one has in mind. We introduce deductive systems, in natural deduction style, for LG’s and show that these systems are normalizable.
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  34.  2
    Definition-Like Extensions by Sorts.Claudia Maria & Paulo S. Veloso - 1995 - Logic Journal of the IGPL 3 (4):579-595.
    Implementation of formal specifications is very important in formal software development and can be described in terms of simple logical concepts. Formal specifications are presentations of theories in many-sorted first-order logic, and an implementation of a formal specification on another formal specification amounts to an interpretation of the former into a conservative extension of the latter. Here we present and analyse some sort introducing constructs akin to those found in many programming languages. This is of importance because it occurs often (...)
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  35. Aspectos de Uma Teoria Geral de Problemas.Paulo As Veloso - 1984 - Cadernos de História E Filosofia da Ciência 7:21-42.
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  36. On conservative and expansive extensions.Paulo Veloso & Sheila Veloso - 1991 - O Que Nos Faz Pensar:87-106.
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  37. On Comparison, Equivalence and Addition of Magnitudes.Paulo A. Veloso, Abel Lassalle-Casanave & Eduardo N. Giovannini - 2019 - Principia: An International Journal of Epistemology 23 (2):153-173.
    A theory of magnitudes involves criteria for their comparison, equivalence and addition. We examine these aspects from an abstract viewpoint, stressing independence and definability. These considerations are triggered by the so-called De Zolt’s principle in the theory of equivalence of plane polygons.
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  38. On Finite and Infinite Fork Algebras and Their Relational Reducts.Paulo As Veloso - 1996 - Logique Et Analyse 39 (154):35-50.
  39. Outlines of a Mathematical Theory of General Problems.Paulo Veloso - 1984 - Philosophia Naturalis 21 (2/4):354-367.
     
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