15 found
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  1.  46
    Display to Labeled Proofs and Back Again for Tense Logics.Agata Ciabattoni, Tim Lyon, Revantha Ramanayake & Alwen Tiu - 2021 - ACM Transactions on Computational Logic 22 (3):1-31.
    We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...)
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  2.  63
    Algebraic Proof Theory for Substructural Logics: Cut-Elimination and Completions.Agata Ciabattoni, Nikolaos Galatos & Kazushige Terui - 2012 - Annals of Pure and Applied Logic 163 (3):266-290.
  3. From Display to Labelled Proofs for Tense Logics.Agata Ciabattoni, Tim Lyon & Revantha Ramanayake - 2018 - In Anil Nerode & Sergei Artemov (eds.), Logical Foundations of Computer Science. Springer International Publishing. pp. 120 - 139.
    We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
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  4.  19
    Algebraic Proof Theory: Hypersequents and Hypercompletions.Agata Ciabattoni, Nikolaos Galatos & Kazushige Terui - 2017 - Annals of Pure and Applied Logic 168 (3):693-737.
  5.  17
    Hypersequent and Display Calculi – a Unified Perspective.Agata Ciabattoni, Revantha Ramanayake & Heinrich Wansing - 2014 - Studia Logica 102 (6):1245-1294.
    This paper presents an overview of the methods of hypersequents and display sequents in the proof theory of non-classical logics. In contrast with existing surveys dedicated to hypersequent calculi or to display calculi, our aim is to provide a unified perspective on these two formalisms highlighting their differences and similarities and discussing applications and recent results connecting and comparing them.
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  6.  46
    Mīmāṃsā Deontic Logic: Proof Theory and Applications.Agata Ciabattoni, Francesco Antonio Genco, Björn Lellmann & Elisa Freschi - 2015 - In Hans De Nivelle (ed.), Automated Reasoning with Analytic Tableaux and Related Methods. Springer. pp. 323--338.
  7.  21
    Understanding Prescriptive Texts: Rules and Logic as Elaborated by the Mīmāṃsā School.Elisa Freschi, Agata Ciabattoni, Francesco A. Genco & Björn Lellmann - 2017 - Journal of World Philosophies 2 (1):47-66.
    The Mīmā ṃ sā school of Indian philosophy elaborated complex ways of interpreting the prescriptive portions of the Vedic sacred texts. The present article is the result of the collaboration of a group of scholars of logic, computer science, European philosophy and Indian philosophy and aims at the individuation and analysis of the deontic system which is applied but never explicitly discussed in Mīmā ṃ sā texts. The article outlines the basic distinction between three sorts of principles —hermeneutic, linguistic and (...)
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  8.  32
    Towards a Semantic Characterization of Cut-Elimination.Agata Ciabattoni & Kazushige Terui - 2006 - Studia Logica 82 (1):95-119.
    We introduce necessary and sufficient conditions for a (single-conclusion) sequent calculus to admit (reductive) cut-elimination. Our conditions are formulated both syntactically and semantically.
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  9.  52
    Finiteness in Infinite-Valued Łukasiewicz Logic.Stefano Aguzzoli & Agata Ciabattoni - 2000 - Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  10. Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Andrei Voronkov & Michel Parigot (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Berlin: Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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  11.  36
    A Proof-Theoretical Investigation of Global Intuitionistic (Fuzzy) Logic.Agata Ciabattoni - 2005 - Archive for Mathematical Logic 44 (4):435-457.
    We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand’s theorem for suitable fragments of GI and GIF.
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  12.  2
    Bounded-Analytic Sequent Calculi and Embeddings for Hypersequent Logics.Agata Ciabattoni, Timo Lang & Revantha Ramanayake - 2021 - Journal of Symbolic Logic 86 (2):635-668.
    A sequent calculus with the subformula property has long been recognised as a highly favourable starting point for the proof theoretic investigation of a logic. However, most logics of interest cannot be presented using a sequent calculus with the subformula property. In response, many formalisms more intricate than the sequent calculus have been formulated. In this work we identify an alternative: retain the sequent calculus but generalise the subformula property to permit specific axiom substitutions and their subformulas. Our investigation leads (...)
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  13.  10
    Mīmāṃsā deontic reasoning using specificity: a proof theoretic approach.Björn Lellmann, Francesca Gulisano & Agata Ciabattoni - 2021 - Artificial Intelligence and Law 29 (3):351-394.
    Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic \. (...)
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  14.  22
    A Sufficient Condition for Completability of Partial Combinatory Algebras.Andrea Asperti & Agata Ciabattoni - 1997 - Journal of Symbolic Logic 62 (4):1209-1214.
    A Partial Combinatory Algebra is completable if it can be extended to a total one. In [1] it is asked (question 11, posed by D. Scott, H. Barendregt, and G. Mitschke) if every PCA can be completed. A negative answer to this question was given by Klop in [12, 11]; moreover he provided a sufficient condition for completability of a PCA (M, ·, K, S) in the form of ten axioms (inequalities) on terms of M. We prove that just one (...)
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  15.  1
    Embedding Formalisms: Hypersequents and Two-Level Systems of Rule.Agata Ciabattoni & Francesco A. Genco - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 197-216.
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