42 found
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  1. Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
    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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  2. 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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  3.  62
    Proof Analysis: A Contribution to Hilbert's Last Problem.Sara Negri & Jan von Plato - 2011 - Cambridge and New York: Cambridge University Press. Edited by Jan Von Plato.
    This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim (...)
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  4. 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. Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):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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  6.  91
    (1 other version)Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 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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  7.  73
    Geometrisation of First-Order Logic.Roy Dyckhoff & Sara Negri - 2015 - Bulletin of Symbolic Logic 21 (2):123-163.
    That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...)
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  8. 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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  9.  76
    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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  10.  30
    Glivenko sequent classes and constructive cut elimination in geometric logics.Giulio Fellin, Sara Negri & Eugenio Orlandelli - 2023 - Archive for Mathematical Logic 62 (5):657-688.
    A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, conservativity for (...)
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  11.  39
    The Gödel-McKinsey-Tarski embedding for infinitary intuitionistic logic and its extensions.Matteo Tesi & Sara Negri - 2023 - Annals of Pure and Applied Logic 174 (8):103285.
  12.  79
    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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  13.  64
    Proof analysis for Lewis counterfactuals.Sara Negri & Giorgio Sbardolini - 2016 - Review of Symbolic Logic 9 (1):44-75.
  14.  13
    Geometric Rules in Infinitary Logic.Sara Negri - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 265-293.
    Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications. Such class of axioms can be translated to inference rules that can be added to a sequent calculus while preserving its structural properties. In this work, this fundamental result is extended to their infinitary generalizations as extensions of sequent calculi for both (...)
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  15. The Church–Fitch knowability paradox in the light of structural proof theory.Paolo Maffezioli, Alberto Naibo & Sara Negri - 2012 - 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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  16.  56
    Proof theory for quantified monotone modal logics.Sara Negri & Eugenio Orlandelli - 2019 - Logic Journal of the IGPL 27 (4):478-506.
    This paper provides a proof-theoretic study of quantified non-normal modal logics. It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced (...)
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  17.  57
    Kripke completeness revisited.Sara Negri - 2009 - In Giuseppe Primiero (ed.), Acts of Knowledge: History, Philosophy and Logic. College Publications. pp. 233--266.
  18.  53
    Conditional beliefs: From neighbourhood semantics to sequent calculus.Marianna Girlando, Sara Negri, Nicola Olivetti & Vincent Risch - 2018 - Review of Symbolic Logic 11 (4):736-779.
    The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...)
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  19. 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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  20.  72
    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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  21. 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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  22.  64
    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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  23.  56
    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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  24.  67
    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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  25.  39
    Glivenko sequent classes in the light of structural proof theory.Sara Negri - 2016 - Archive for Mathematical Logic 55 (3-4):461-473.
    In 1968, Orevkov presented proofs of conservativity of classical over intuitionistic and minimal predicate logic with equality for seven classes of sequents, what are known as Glivenko classes. The proofs of these results, important in the literature on the constructive content of classical theories, have remained somehow cryptic. In this paper, direct proofs for more general extensions are given for each class by exploiting the structural properties of G3 sequent calculi; for five of the seven classes the results are strengthened (...)
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  26. 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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  27.  83
    Tychonoff's theorem in the framework of formal topologies.Sara Negri & Silvio Valentini - 1997 - Journal of Symbolic Logic 62 (4):1315-1332.
  28. Decision methods for linearly ordered Heyting algebras.Sara Negri & Roy Dyckhoff - 2006 - 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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  29.  32
    The intensional side of algebraic-topological representation theorems.Sara Negri - 2017 - Synthese 198 (Suppl 5):1121-1143.
    Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic (...)
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  30.  24
    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. Boston: De Gruyter. pp. 269-290.
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  31.  12
    A terminating intuitionistic calculus.Giulio Fellin & Sara Negri - forthcoming - Journal of Symbolic Logic:1-21.
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  32.  31
    Alternative Axiomatization for Logics of Agency in a G3 Calculus.Sara Negri & Edi Pavlović - 2021 - Foundations of Science 28 (1):205-224.
    In a recent paper, Negri and Pavlović (Studia Logica 1–35, 2020) have formulated a decidable sequent calculus for the logic of agency, specifically for a deliberative see-to-it-that modality, or dstit. In that paper the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (Facing the future: agents and choices in our indeterminist world. Oxford University Press, Oxford, 2001). And while the influence of the latter book on the study of logics (...)
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  33.  26
    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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  34. Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX 2021.Anupam Das & Sara Negri (eds.) - 2021
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  35. TABLEAUX 2021, LNAI 12842.Anupam Das & Sara Negri (eds.) - 2021
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  36.  84
    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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  37.  21
    The Logic of Conditional Beliefs: Neighbourhood Semantics and Sequent Calculus.Marianna Girlando, Sara Negri, Nicola Olivetti & Vincent Risch - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 322-341.
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  38.  2
    G3-style Sequent Calculi for Gurevich Logic and Its Neighbors.Norihiro Kamide & Sara Negri - forthcoming - Studia Logica:1-29.
    G3-style sequent calculi are introduced for a family of logics with strong negation: Gurevich logic, Nelson logic, intuitionistic propositional logic, Avron logic, De-Omori logic, and classical propositional logic. Structural properties including cut elimination are established for these calculi. In addition, a Glivenko theorem for embedding classical propositional logic into Gurevich logic is shown.
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  39.  2
    A Proof-Theoretic Approach to Formal Epistemology.Sara Negri & Edi Pavlović - 2024 - In Yale Weiss & Romina Birman (eds.), Saul Kripke on Modal Logic. Cham: Springer. pp. 303-345.
    Ever since antiquity, attempts have been made at defining knowledge through belief augmented by additional properties such as truth and justification. These characterizations have been challenged by Gettier counterexamples and their variants. A modern proposal, what is known as defeasibility theory, characterizes knowledge through stability under revision of beliefs on the basis of true or arbitrary information. A formal investigation of such a proposal calls for the methods of dynamic epistemic logic: well developed semantic approaches to dynamic epistemic logic have (...)
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  40.  23
    Recent Advances in Proof Systems for Modal Logic.Sara Negri - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10: Papers From the Tenth Aiml Conference, Held in Groningen, the Netherlands, August 2014. London, England: CSLI Publications. pp. 421-422.
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  41. Advances in Modal Logic 13. Booklet of Short Papers.Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.) - 2020 - Helsinki:
     
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  42.  48
    Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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