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“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic
Studies in Logic, Grammar and Rhetoric, 2021 In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks
Pogonowski Jerzy
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de Finetti's coherence and exchangeability in infinitary logic
International Journal of Approximate Reasoning, 2022 We continue the investigation towards a logic-based approach to statistics within the infinitary conservative extension of (cid:32)Lukasiewicz logic IRL and prove versions of de Finetti’s theorems on coherence and exchangeability.
Serafina Lapenta
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On the Proof Theory of Infinitary Modal Logic
Studia Logica, 2022 The article deals with infinitary modal logic. We first discuss the difficulties related to the development of a satisfactory proof theory and then we show how to overcome these problems by introducing a labelled sequent calculus which is sound and ...
Matteo Tesi
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An infinitary propositional probability logic
Archive for Mathematical Logic, 2022 We introduce a logic for a class of probabilistic Kripke structures that we call type structures, as they are inspired by Harsanyi type spaces. The latter structures are used in theoretical economics and game theory.
Stefano Baratella
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Axiomatizations of universal classes through infinitary logic
Algebra Universalis, 2018 We present a scheme for providing axiomatizations of universal classes. We use infinitary sentences there. New proofs of Birkhoff’s $$\mathsf {HSP}$$HSP-theorem and Mal’cev’s $$\mathsf {SPP_U}$$SPPU-theorem are derived.
Michał Stronkowski
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Encoding many-valued logic in $\lambda$-calculus [PDF]
Logical Methods in Computer Science, 2021 We will extend the well-known Church encoding of Boolean logic into $\lambda$-calculus to an encoding of McCarthy's $3$-valued logic into a suitable infinitary extension of $\lambda$-calculus that identifies all unsolvables by $\bot$, where $\bot$ is a ...
Fer-Jan de Vries
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INFINITARY LOGIC HAS NO EXPRESSIVE EFFICIENCY OVER FINITARY LOGIC [PDF]
Journal of Symbolic Logic (JSL), 2022 We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi $ (in $\mathcal {L}_{\omega ,\omega }$ ) is equivalent to
Matthew Harrison-Trainor +1 more
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Finitary Simulation of Infinitary $\beta$-Reduction via Taylor Expansion, and Applications [PDF]
Logical Methods in Computer Science, 2023 Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation theorem relating
Rémy Cerda, Lionel Vaux Auclair
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Infinitary logic with infinite sequents: syntactic investigations
Mathematical Logic Quarterly, 2023 The present paper deals with a purely syntactic analysis of infinitary logic with infinite sequents. In particular, we discuss sequent calculi for classical and intuitionistic infinitary logic with good structural properties based on sequents possibly ...
Matteo Tesi
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Quantifying over Boolean announcements [PDF]
Logical Methods in Computer Science, 2022 Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL.
Hans van Ditmarsch, Tim French
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