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  1. On Dummett’s verificationist justification procedure.Wagner de Campos Sanz & Hermógenes Oliveira - 2016 - Synthese 193 (8):2539-2559.
    We examine the proof-theoretic verificationist justification procedure proposed by Dummett. After some scrutiny, two distinct interpretations with respect to bases are advanced: the independent and the dependent interpretation. We argue that both are unacceptable as a semantics for propositional intuitionistic logic.
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  • The Bounds of Logic: A Generalized Viewpoint.Gila Sher - 1991 - MIT Press.
    The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...)
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  • Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
    We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...)
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  • Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
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  • Which ‘Intensional Paradoxes’ are Paradoxes?Neil Tennant - 2024 - Journal of Philosophical Logic 53 (4):933-957.
    We begin with a brief explanation of our proof-theoretic criterion of paradoxicality—its motivation, its methods, and its results so far. It is a proof-theoretic account of paradoxicality that can be given in addition to, or alongside, the more familiar semantic account of Kripke. It is a question for further research whether the two accounts agree in general on what is to count as a paradox. It is also a question for further research whether and, if so, how the so-called Ekman (...)
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  • Meaning and identity of proofs in a bilateralist setting: A two-sorted typed lambda-calculus for proofs and refutations.Sara Ayhan - forthcoming - Journal of Logic and Computation.
    In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...)
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  • What are acceptable reductions? Perspectives from proof-theoretic semantics and type theory.Sara Ayhan - 2023 - Australasian Journal of Logic 20 (3):412-428.
    It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...)
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  • Uniqueness of Logical Connectives in a Bilateralist Setting.Sara Ayhan - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 1-16.
    In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of (...)
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  • Methodological deflationism and metaphysical grounding: from because via truth to ground.Johannes Stern - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    The paper proposes a strategy for understanding metaphysical grounding in deflationary terms and, more generally, proposes a form of methodological deflationism with respect to the notions of ground. The idea is to define a deflationary is grounded in-predicate by appeal to the two-place non-causal connective ‘because’ and a deflationary truth predicate. To this end, we discuss the explanatory role of the truth-predicate in non-causal explanations and develop a theory of truth for the language of the ‘because’-connective. We argue that at (...)
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  • The Formalization of Arguments.Robert Michels - 2020 - Dialectica 74 (2).
    The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such formalizations, (...)
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  • The Subject Matter of Logic: Explaining what logic is about.Elizabeth Olsen - 2021 - Dissertation, Victoria University of Wellington
    Logicians disagree about how validity—the very heart of logic—should be understood. Many different formal systems have been born due to this disagreement. This thesis examines how teachers explain the subject matter of logic to students in introductory logic textbooks, and demonstrates the different explanations teachers use. These differences help explain why logicians have different intuitions about validity.
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  • (1 other version)Subatomic Inferences: An Inferentialist Semantics for Atomics, Predicates, and Names.Kai Tanter - 2021 - Review of Symbolic Logic:1-28.
    Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s (...)
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  • Advances in Natural Deduction: A Celebration of Dag Prawitz's Work.Luiz Carlos Pereira & Edward Hermann Haeusler (eds.) - 2012 - Dordrecht, Netherland: Springer.
    This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...)
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  • Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules.Nils Kürbis - 2021 - Synthese 199 (5-6):14223-14248.
    This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that deductions (...)
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  • Proofs, Grounds and Empty Functions: Epistemic Compulsion in Prawitz’s Semantics.Antonio Piccolomini D’Aragona - 2021 - Journal of Philosophical Logic 51 (2):249-281.
    Prawitz has recently developed a theory of epistemic grounding that differs in many respects from his earlier semantics of arguments and proofs. An innovative approach to inferences yields a new conception of the intertwinement of the notions of valid inference and proof. We aim at singling out three reasons that may have led Prawitz to the ground-theoretic turn, i.e.: a better order in the explanation of the relation between valid inferences and proofs; a notion of valid inference based on which (...)
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  • Proof-Theoretic Semantics and Inquisitive Logic.Will Stafford - 2021 - Journal of Philosophical Logic 50 (5):1199-1229.
    Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination (...)
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  • Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  • On the notion of validity for the bilateral classical logic.Ukyo Suzuki & Yoriyuki Yamagata - manuscript
    This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound and complete respect to (...)
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  • (1 other version)Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
    This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...)
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  • Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    This volume is the first ever collection devoted to the field of proof-theoretic 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, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term (...)
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  • Hopeful Monsters: A Note on Multiple Conclusions.Bogdan Dicher - 2020 - Erkenntnis 85 (1):77-98.
    Arguments, the story goes, have one or more premises and only one conclusion. A contentious generalisation allows arguments with several disjunctively connected conclusions. Contentious as this generalisation may be, I will argue nevertheless that it is justified. My main claim is that multiple conclusions are epiphenomena of the logical connectives: some connectives determine, in a certain sense, multiple-conclusion derivations. Therefore, such derivations are completely natural and can safely be used in proof-theoretic semantics.
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  • On the explanatory power of truth in logic.Gila Sher - 2018 - Philosophical Issues 28 (1):348-373.
    Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal force, generality, (...)
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  • Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General.Ross T. Brady - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):755--781.
    This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.
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  • Completeness of Second-Order Intuitionistic Propositional Logic with Respect to Phase Semantics for Proof-Terms.Yuta Takahashi & Ryo Takemura - 2019 - Journal of Philosophical Logic 48 (3):553-570.
    Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard’s phase semantics so that it became phase semantics for proof-terms, i.e., lambda-terms. They formulated phase semantics for proof-terms of Laird’s dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird’s calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this paper, (...)
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  • Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai F. Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...)
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  • A novel approach to equality.Andrzej Indrzejczak - 2021 - Synthese 199 (1-2):4749-4774.
    A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...)
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  • From Curry to Haskell.Felice Cardone - 2020 - Philosophy and Technology 34 (1):57-74.
    We expose some basic elements of a style of programming supported by functional languages like Haskell by relating them to a coherent set of notions and techniques from Curry’s work in combinatory logic and formal systems, and their algebraic and categorical interpretations. Our account takes the form of a commentary to a simple fragment of Haskell code attempting to isolate the conceptual sources of the linguistic abstractions involved.
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  • (1 other version)The original sin of proof-theoretic semantics.Bogdan Dicher & Francesco Paoli - 2020 - Synthese:1-26.
    Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...)
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  • DEFLATIONARY TRUTH: CONSERVATIVITY OR LOGICALITY?Henri Galinon - 2015 - Philosophical Quarterly 65 (259):268-274.
    It has been argued in the literature that the deflationists’ thesis about the dispensability of truth as an explanatory notion forces them to adopt a conservative theory of truth. I suggest that the deflationists’ claim that the notion of truth is akin to a logical notion should be taken more seriously. This claim casts some doubts on the adequacy of the conservativity requirement, while it also calls for further investigation to assess its philosophical plausibility.
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  • Anti-realistic Notions of Truth.Luca Tranchini - 2012 - Topoi 31 (1):5-8.
    Validity, the central concept of the so-called ‘proof-theoretic semantics’ is described as correctly applying to the arguments that denote proofs. In terms of validity, I propose an anti-realist characterization of the notions of truth and correct assertion, at the core of which is the idea that valid arguments may fail to be recognized as such. The proposed account is compared with Dummett’s and Prawitz’s views on the matter.
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  • Tarskian consequence relations bilaterally: some familiar notions.Sergey Drobyshevich - 2019 - Synthese 198 (S22):5213-5240.
    This paper is dedicated to developing a formalism that takes rejection seriously. Bilateral notation of signed formulas with force indicators is adopted to define signed consequences which can be viewed as the bilateral counterpart of Tarskian consequence relations. Its relation to some other bilateral approaches is discussed. It is shown how David Nelson’s logic N4 can be characterized bilaterally and the corresponding completeness result is proved. Further, bilateral variants of three familiar notions are considered and investigated: that of a fragment, (...)
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  • (1 other version)Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
    This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...)
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  • Kant’s Die falsche Spitzfindigkeit and Proof-theoretic Semantics.Tiago Rezende de Castro Alves - 2022 - History and Philosophy of Logic 44 (3):273-286.
    According to Schroeder-Heister 2018, proof-theoretic semantics is ‘an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof. Proof-theoretic semantics also means the semantics of proofs, i.e. the semantics of entities which describe how we arrive at certain assertions given (...)
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  • Grounding rules and (hyper-)isomorphic formulas.Francesca Poggiolesi - 2020 - Australasian Journal of Logic 17 (1):70-80.
    An oft-defended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called proof-theoretic semantics, see Schroeder- Heister (1991); Prawitz (2006). A branch of proof-theoretic semantics, mainly developed by Dosen (2019); Dosen and Petric (2011), isolates in a precise mathematical manner formulas (of a logic L) that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The (...)
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  • Adjectival and Adverbial Modification: The View from Modern Type Theories.Stergios Chatzikyriakidis & Zhaohui Luo - 2017 - Journal of Logic, Language and Information 26 (1):45-88.
    In this paper we present a study of adjectival/adverbial modification using modern type theories, i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented given their proof-theoretic nature. In MTT-semantics, common (...)
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • The Problem of Natural Representation of Reasoning in the Lvov-Warsaw School.Andrzej Indrzejczak - 2024 - History and Philosophy of Logic 45 (2):142-160.
    The problem of precise characterisation of traditional forms of reasoning applied in mathematics was independently investigated and successfully resolved by Jaśkowski and Gentzen in 1934. However, there are traces of earlier interests in this field exhibited by the members of the Lvov-Warsaw School. We focus on the results obtained by Jaśkowski and Leśniewski. Jaśkowski provided the first formal system of natural deduction in 1926. Leśniewski also demonstrated in some of his papers how to construct proofs in accordance with intuitively correct (...)
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  • Failure of Completeness in Proof-Theoretic Semantics.Thomas Piecha, Wagner de Campos Sanz & Peter Schroeder-Heister - 2015 - Journal of Philosophical Logic 44 (3):321-335.
    Several proof-theoretic 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. Our central result shows that Harrop’s rule (...)
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  • (1 other version)Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof.Francesca Poggiolesi & Francesco Genco - 2021 - Erkenntnis:1-27.
    This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...)
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  • Inferentialism and Structuralism: A Tale of Two Theories.Ryan Mark Nefdt - 2018 - Logique Et Analyse 61 (244):489-512.
    This paper aims to unite two seemingly disparate themes in the philosophy of mathematics and language respectively, namely ante rem structuralism and inferentialism. My analysis begins with describing both frameworks in accordance with their genesis in the work of Hilbert. I then draw comparisons between these philosophical views in terms of their similar motivations and similar objections to the referential orthodoxy. I specifically home in on two points of comparison, namely the role of norms and the relation of ontological dependence (...)
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  • Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.Bartosz Więckowski - 2016 - Journal of Logic, Language and Information 25 (2):215-268.
    A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...)
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  • State-Based Modal Logics for Free Choice.Maria Aloni, Aleksi Anttila & Fan Yang - 2024 - Notre Dame Journal of Formal Logic -1:1-47.
    We study the mathematical properties of bilateral state-based modal logic (BSML), a modal logic employing state-based semantics (also known as team semantics), which has been used to account for free choice inferences and related linguistic phenomena. This logic extends classical modal logic with a nonemptiness atom which is true in a state if and only if the state is nonempty. We introduce two extensions of BSML and show that the extensions are expressively complete, and develop natural deduction axiomatizations for the (...)
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  • Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
    In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...)
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  • Natural Deduction Bottom Up.Ernst Zimmermann - 2021 - Journal of Logic, Language and Information 30 (3):601-631.
    The paper introduces a new type of rules into Natural Deduction, elimination rules by composition. Elimination rules by composition replace usual elimination rules in the style of disjunction elimination and give a more direct treatment of additive disjunction, multiplicative conjunction, existence quantifier and possibility modality. Elimination rules by composition have an enormous impact on proof-structures of deductions: they do not produce segments, deduction trees remain binary branching, there is no vacuous discharge, there is only few need of permutations. This new (...)
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  • Subatomic Negation.Bartosz Więckowski - 2021 - Journal of Logic, Language and Information 30 (1):207-262.
    The operators of first-order logic, including negation, operate on whole formulae. This makes it unsuitable as a tool for the formal analysis of reasoning with non-sentential forms of negation such as predicate term negation. We extend its language with negation operators whose scope is more narrow than an atomic formula. Exploiting the usefulness of subatomic proof-theoretic considerations for the study of subatomic inferential structure, we define intuitionistic subatomic natural deduction systems which have several subatomic operators and an additional operator for (...)
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  • (1 other version)Reprint of: A more general general proof theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic (...)
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  • On a Generality Condition in Proof‐Theoretic Semantics.Bogdan Dicher - 2017 - Theoria 83 (4):394-418.
    In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...)
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  • Constructive belief reports.Bartosz Więckowski - 2015 - Synthese 192 (3):603-633.
    The paper develops a proof-theoretic semantics for belief reports by extending the constructive type-theoretical formalism presented in Więckowski with a specific kind of set-forming operator suited for the representation of belief attitudes. The extended formalism allows us to interpret constructions which involve, e.g., iteration of belief, quantifying into belief contexts, and anaphora in belief reports. Moreover, constructive solutions to canonical instances of the problem of hyperintensionality are suggested. The paper includes a discussion of Ranta’s constructive account of belief reports.
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  • The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics.Peter Schroeder-Heister - 2012 - Synthese 187 (3):925-942.
    The hypothetical notion of consequence is normally understood as the transmission of a categorical notion from premisses to conclusion. In model-theoretic semantics this categorical notion is 'truth', in standard proof-theoretic semantics it is 'canonical provability'. Three underlying dogmas, (I) the priority of the categorical over the hypothetical, (II) the transmission view of consequence, and (III) the identification of consequence and correctness of inference are criticized from an alternative view of proof-theoretic semantics. It is argued that consequence is a basic semantical (...)
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