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Tim Lyon
Vienna University of Technology
  1.  37
    The Basics of Display Calculi.Tim Lyon, Christian Ittner, Timo Eckhardt & Norbert Gratzl - 2017 - Kriterion - Journal of Philosophy 31 (2):55-100.
    The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.
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  2.  88
    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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  3.  16
    Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic Via Nested Sequents.Tim Lyon, Alwen Tiu, Rajeev Gore & Ranald Clouston - 2020 - In Maribel Fernandez & Anca Muscholl (eds.), 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Dagstuhl, Germany: pp. 1-16.
    We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...)
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  4.  56
    Cut-Free Calculi and Relational Semantics for Temporal STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In Francesco Calimeri, Nicola Leone & Marco Manna (eds.), Logics in Artificial Intelligence. Springer International Publishing. pp. 803 - 819.
    We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.
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  5.  29
    Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic Via Linear Nested Sequents.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 156-176.
    This paper employs the linear nested sequent framework to design a new cut-free calculus (LNIF) for intuitionistic fuzzy logic---the first-order Goedel logic characterized by linear relational frames with constant domains. Linear nested sequents---which are nested sequents restricted to linear structures---prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.
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  6.  22
    On Deriving Nested Calculi for Intuitionistic Logics From Semantic Systems.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 177-194.
    This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...)
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  7.  29
    Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In M. Baldoni, M. Dastani, B. Liao, Y. Sakurai & R. Zalila Wenkstern (eds.), PRIMA 2019: Principles and Practice of Multi-Agent Systems. 93413 Cham, Germany: Springer. pp. 202-218.
    This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we (...)
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  8.  27
    A Neutral Temporal Deontic STIT Logic.Kees van Berkel & Tim Lyon - 2019 - In P. Blackburn, E. Lorini & M. Guo (eds.), Logic, Rationality, and Interaction. Berlin, Heidelberg: pp. 340-354.
    In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving (...)
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