
15Karl Popper on DeductionIn Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction, Springer Verlag. pp. 301321. 2024.We outline Karl Popper’s theory of deduction, which he developed in the 1940s. In his theory it is assumed that a consequence relation is given or otherwise constructed by postulation. Logical operations, which may be available in this consequence relation, are then characterized by means of relational definitions, and logical operators are introduced as names for these operations by means of inferential definitions. Using logically structured sentences thus introduced, the inference laws for th…Read more

63Peter SchroederHeister on ProofTheoretic Semantics (edited book)Springer. 2024.This open access book is a superb collection of some fifteen chapters inspired by SchroederHeister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by SchroederHeister himself. For several decades, Peter SchroederHeister has been a central figure in prooftheoretic semantics, a field of study situated at the interface of logic, theoretical computer science, naturallanguage semantics, and the philosophy o…Read more

Atomic Systems in ProofTheoretic Semantics: Two ApproachesIn Ángel Nepomuceno Fernández, Olga Pombo Martins & Juan Redmond (eds.), Epistemology, Knowledge and the Impact of Interaction, Springer Verlag. 2016.

Completeness in ProofTheoretic SemanticsIn Peter SchroederHeister & Thomas Piecha (eds.), Advances in ProofTheoretic Semantics, Springer Verlag. 2015.

41Advances in ProofTheoretic Semantics (edited book)Springer Verlag. 2015.This volume is the first ever collection devoted to the field of prooftheoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, prooftheoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and th…Read more

Advances in ProofTheoretic Semantics: IntroductionIn Peter SchroederHeister & Thomas Piecha (eds.), Advances in ProofTheoretic Semantics, Springer Verlag. 2015.

58General Proof Theory: IntroductionStudia Logica 107 (1): 15. 2019.This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.

2Beyond Logic. Proceedings of the Conference held in CerisylaSalle, 2227 May 2017 (edited book). 2017.

43Incompleteness of Intuitionistic Propositional Logic with Respect to ProofTheoretic SemanticsStudia Logica 107 (1): 233246. 2019.Prawitz proposed certain notions of prooftheoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any prooftheoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning…Read more

21A Critical Remark on the BHK Interpretation of ImplicationPhilosophia Scientiae 18 1322. 2014.On analyse l’interprétation BHK de constantes logiques sur la base d’une prise en compte systématique de Prawitz, résultant en une reformulation de l’interprétation BHK dans laquelle l’assertabilité de propositions atomiques est déterminée par des systèmes de Post. On démontre que l’interprétation BHK reformulée rend davantage de propositions assertables que la logique propositionnelle intuitionniste rend prouvable. La loi de Mints est examinée en tant qu’exemple d’une telle proposition. La logi…Read more

48Popper's Notion of Duality and His Theory of NegationsHistory and Philosophy of Logic 38 (2): 154189. 2017.Karl Popper developed a theory of deductive logic in the late 1940s. In his approach, logic is a metalinguistic theory of deducibility relations that are based on certain purely structural rules. Logical constants are then characterized in terms of deducibility relations. Characterizations of this kind are also called inferential definitions by Popper. In this paper, we expound his theory and elaborate some of his ideas and results that in some cases were only sketched by him. Our focus is on Po…Read more

30Constructive semantics, admissibility of rules and the validity of Peirce's lawLogic Journal of the IGPL 22 (2): 297308. 2014.

88Failure of Completeness in ProofTheoretic SemanticsJournal of Philosophical Logic 44 (3): 321335. 2015.Several prooftheoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Ou…Read more

47Inversion by definitional reflection and the admissibility of logical rulesReview of Symbolic Logic 2 (3): 550569. 2009.The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & SchroederHeister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by SchroederHeister . Using the framework of definitional reflection and its admissibility interpretation, we show th…Read more

21Dialogical Logic. 2015.Dialogical Logic Dialogical logic is an approach to logic in which the meaning of the logical constants and the notion of validity are explained in gametheoretic terms. The meaning of logical constants like “and”, “or”, “implies”, “not”, “every”, and so forth, is given in terms of how assertions containing these logical constants can … Continue reading Dialogical Logic →.