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23Alternative Axiomatization for Logics of Agency in a G3 CalculusFoundations of Science 28 (1): 205-224. 2021.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 …Read more
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22University of Azores, Ponta Delgada, Azores, Portugal June 30–July 4, 2010Bulletin of Symbolic Logic 17 (3). 2011.
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19Equality in the Presence of Apartness: An Application of Structural Proof Analysis to Intuitionistic AxiomaticsPhilosophia Scientiae 61-79. 2006.The theories of apartness, equality, and n-stable equality are presented through contraction- and cut-free sequent calculi. By methods of proof analysis, a purely proof-theoretic characterization of the equality fragment of apartness is obtained.
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19Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line ConstructionIn Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science, De Gruyter. pp. 269-290. 2016.
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18Glivenko sequent classes and constructive cut elimination in geometric logicsArchive for Mathematical Logic 62 (5): 657-688. 2023.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…Read more
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17Tychonoff's Theorem in the Framework of Formal TopologiesJournal of Symbolic Logic 62 (4): 1315-1332. 1997.
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17Equality in the Presence of Apartness: An Application of Structural Proof Analysis to Intuitionistic AxiomaticsPhilosophia Scientiae 61-79. 2006.The theories of apartness, equality, and n-stable equality are presented through contraction- and cut-free sequent calculi. By methods of proof analysis, a purely proof-theoretic characterization of the equality fragment of apartness is obtained.
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16The Logic of Conditional Beliefs: Neighbourhood Semantics and Sequent CalculusIn Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, Csli Publications. pp. 322-341. 2016.
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15Recent Advances in Proof Systems for Modal LogicIn Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10, Csli Publications. pp. 421-422. 2014.
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15Proof-Theoretic Analysis of the Logics of Agency: The Deliberative STITStudia Logica 109 (3): 473-507. 2020.A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.
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14Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic LogicJournal of Symbolic Logic 65 (4): 1499-1518. 2000.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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8Admissibility of structural rules for extensions of contraction-free sequent calculiLogic Journal of the IGPL 9 (4): 541-548. 2001.The contraction-free sequent calculus G4 for intuitionistic logic is extended by rules following a general rule-scheme for nonlogical axioms. Admissibility of structural rules for these extensions is proved in a direct way by induction on derivations. This method permits the representation of various applied logics as complete, contraction- and cut-free sequent calculus systems with some restrictions on the nature of the derivations. As specific examples, intuitionistic theories of apartness and…Read more
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7Sequent Calculus in Natural Deduction StyleJournal of Symbolic Logic 66 (4): 1803-1816. 2001.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. Therefo…Read more
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7Geometric Rules in Infinitary LogicIn Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer Verlag. pp. 265-293. 2021.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 extensi…Read more
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A proof theoretical perspective on public announcement logicLogic and Philosophy of Science. forthcoming.
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Natural deduction and normal form for intuitionistic linear logicArchive for Mathematical Logic. forthcoming.