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Profile: Sara Negri (University of Helsinki)
  1.  27
    Proof Analysis in Intermediate Logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1-2):71-92.
    Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...)
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  2.  13
    Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
    Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class (...)
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  3.  80
    The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory.Paolo Maffezioli, Alberto Naibo & Sara Negri - 2013 - Synthese 190 (14):2677-2716.
    Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...)
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  4.  43
    Does the Deduction Theorem Fail for Modal Logic?Raul Hakli & Sara Negri - 2012 - Synthese 187 (3):849-867.
    Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a way that (...)
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  5.  41
    Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
    The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.
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  6.  8
    Contraction-Free Sequent Calculi for Geometric Theories with an Application to Barr's Theorem.Sara Negri - 2003 - Archive for Mathematical Logic 42 (4):389-401.
    Geometric theories are presented as contraction- and cut-free systems of sequent calculi with mathematical rules following a prescribed rule-scheme that extends the scheme given in Negri and von Plato. Examples include cut-free calculi for Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric implication is classically derivable from a geometric theory then it is intuitionistically derivable.
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  7.  37
    Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
    A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.
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  8. Sequent Calculus in Natural Deduction Style.Sara Negri & Jan von Plato - 2001 - Journal of Symbolic Logic 66 (4):1803-1816.
    A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...)
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  9.  13
    The Continuum as a Formal Space.Sara Negri & Daniele Soravia - 1999 - Archive for Mathematical Logic 38 (7):423-447.
    A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.
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  10.  10
    Kripke Completeness Revisited.Sara Negri - 2009 - In Giuseppe Primiero (ed.), Acts of Knowledge: History, Philosophy and Logic. College Publications. pp. 233--266.
  11.  7
    Sequent Calculus Proof Theory of Intuitionistic Apartness and Order Relations.Sara Negri - 1999 - Archive for Mathematical Logic 38 (8):521-547.
    Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apartness, for sequents in which all atomic formulas appear negated. The proof extends to conservativity results for the theories of constructive order over (...)
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  12.  6
    A Normalizing System of Natural Deduction for Intuitionistic Linear Logic.Sara Negri - 2002 - Archive for Mathematical Logic 41 (8):789-810.
    The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.
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  13.  28
    Reasoning About Collectively Accepted Group Beliefs.Raul Hakli & Sara Negri - 2011 - Journal of Philosophical Logic 40 (4):531-555.
    A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction- and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. Completeness with (...)
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  14.  19
    Proof Analysis for Lewis Counterfactuals.Sara Negri & Giorgio Sbardolini - forthcoming - Review of Symbolic Logic:1-32.
  15.  7
    Tychonoff's Theorem in the Framework of Formal Topologies.Sara Negri & Silvio Valentini - 1997 - Journal of Symbolic Logic 62 (4):1315-1332.
  16.  28
    Cut Elimination in the Presence of Axioms.Negri Sara & Plato Jan Von - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
    A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...)
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  17.  20
    Varieties of Linear Calculi.Sara Negri - 2002 - Journal of Philosophical Logic 31 (6):569-590.
    A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from (...)
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  18.  14
    Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
    Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...)
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  19.  2
    Proof-Theoretical Analysis of Order Relations.Sara Negri, Jan von Plato & Thierry Coquand - 2004 - Archive for Mathematical Logic 43 (3):297-309.
    A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.
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  20.  3
    Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line Construction.Jan von Plato & Sara Negri - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. De Gruyter. pp. 269-290.
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  21.  6
    Glivenko Sequent Classes in the Light of Structural Proof Theory.Sara Negri - forthcoming - Archive for Mathematical Logic.
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  22.  3
    Geometrisation of First-Order Logic.Roy Dyckhoff & Sara Negri - 2015 - Bulletin of Symbolic Logic 21 (2):123-163.
  23.  15
    Decision Methods for Linearly Ordered Heyting Algebras.Sara Negri & Roy Dyckhoff - 2005 - Archive for Mathematical Logic 45 (4):411-422.
    The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.
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  24.  9
    For Oiva Ketonen's 85th Birthday.Sara Negri & Jan von Plato - 1998 - Bulletin of Symbolic Logic 4 (4).
  25.  21
    Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic.Roy Dyckhoff & Sara Negri - 2000 - Journal of Symbolic Logic 65 (4):1499-1518.
    We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.
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  26.  2
    University of Azores, Ponta Delgada, Azores, Portugal June 30–July 4, 2010.Eric Allender, José L. Balcázar, Shafi Goldwasser, Denis Hirschfeldt, Sara Negri, Toniann Pitassi & Ronald de Wolf - 2011 - Bulletin of Symbolic Logic 17 (3).
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  27.  1
    Equality in the Presence of Apartness: An Application of Structural Proof Analysis to Intuitionistic Axiomatics.Bianca Boretti & Sara Negri - 2006 - Philosophia Scientiae:61-79.
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  28. Equality in the Presence of Apartness: An Application of Structural Proof Analysis to Intuitionistic Axiomatics.Bianca Boretti & Sara Negri - 2006 - Philosophia Scientae:61-79.
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  29. Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic.Roy Dyckhoff & Sara Negri - 2000 - Journal of Symbolic Logic 65 (4):1499-1518.
    We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.
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  30.  15
    Proof Analysis: A Contribution to Hilbert's Last Problem.Sara Negri & Jan von Plato - 2011 - Cambridge University Press.
    Machine generated contents note: Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; Part IV. Proof Systems for Nonclassical (...)
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  31. Tychonoff's Theorem in the Framework of Formal Topologies.Sara Negri & Silvio Valentini - 1997 - Journal of Symbolic Logic 62 (4):1315-1332.
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