Relevant bibliographies by topics / Proof-theoretic semantics

Academic literature on the topic 'Proof-theoretic semantics'

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Published: 10 March 2023

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Journal articles on the topic "Proof-theoretic semantics"

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Kahle, Reinhard, and Peter Schroeder-Heister. "Introduction: Proof-theoretic Semantics." Synthese 148, no. 3 (February 2006): 503–6. http://dx.doi.org/10.1007/s11229-004-6292-5.

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Francez, Nissim. "Views of proof-theoretic semantics: reified proof-theoretic meanings." Journal of Logic and Computation 26, no. 2 (May 30, 2014): 479–94. http://dx.doi.org/10.1093/logcom/exu035.

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Francez, Nissim. "Bilateralism in Proof-Theoretic Semantics." Journal of Philosophical Logic 43, no. 2-3 (January 10, 2013): 239–59. http://dx.doi.org/10.1007/s10992-012-9261-3.

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Stafford, Will. "Proof-Theoretic Semantics and Inquisitive Logic." Journal of Philosophical Logic 50, no. 5 (June 12, 2021): 1199–229. http://dx.doi.org/10.1007/s10992-021-09596-7.

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Chung, Inkyo. "Proof-Theoretic Semantics and Atomic Base." Korean Journal of Philosophy 125 (November 30, 2015): 57. http://dx.doi.org/10.18694/kjp.2015.11.125.57.

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Stirton, William R. "SOME PROBLEMS FOR PROOF-THEORETIC SEMANTICS." Philosophical Quarterly 58, no. 231 (April 2008): 278–98. http://dx.doi.org/10.1111/j.1467-9213.2007.506.x.

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Francez, Nissim, Roy Dyckhoff, and Gilad Ben-Avi. "Proof-Theoretic Semantics for Subsentential Phrases." Studia Logica 94, no. 3 (March 24, 2010): 381–401. http://dx.doi.org/10.1007/s11225-010-9241-y.

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Francez, Nissim, and Michael Kaminski. "A Proof-Theoretic Semantics for Exclusion." Logica Universalis 11, no. 4 (October 24, 2017): 489–505. http://dx.doi.org/10.1007/s11787-017-0179-y.

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Tait, William W. "Proof-theoretic Semantics for Classical Mathematics." Synthese 148, no. 3 (February 2006): 603–22. http://dx.doi.org/10.1007/s11229-004-6271-x.

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Schroeder-Heister, Peter. "Validity Concepts in Proof-theoretic Semantics." Synthese 148, no. 3 (February 2006): 525–71. http://dx.doi.org/10.1007/s11229-004-6296-1.

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Dissertations / Theses on the topic "Proof-theoretic semantics"

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Martin, Alan J. "Reasoning Using Higher-Order Abstract Syntax in a Higher-Order Logic Proof Environment: Improvements to Hybrid and a Case Study." Thesis, Université d'Ottawa / University of Ottawa, 2010. http://hdl.handle.net/10393/19711.

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We present a series of improvements to the Hybrid system, a formal theory implemented in Isabelle/HOL to support specifying and reasoning about formal systems using higher-order abstract syntax (HOAS). We modify Hybrid's type of terms, which is built definitionally in terms of de Bruijn indices, to exclude at the type level terms with `dangling' indices. We strengthen the injectivity property for Hybrid's variable-binding operator, and develop rules for compositional proof of its side condition, avoiding conversion from HOAS to de Bruijn indices. We prove representational adequacy of Hybrid (with these improvements) for a lambda-calculus-like subset of Isabelle/HOL syntax, at the level of set-theoretic semantics and without unfolding Hybrid's definition in terms of de Bruijn indices. In further work, we prove an induction principle that maintains some of the benefits of HOAS even for open terms. We also present a case study of the formalization in Hybrid of a small programming language, Mini-ML with mutable references, including its operational semantics and a type-safety property. This is the largest case study in Hybrid to date, and the first to formalize a language with mutable references. We compare four variants of this formalization based on the two-level approach adopted by Felty and Momigliano in other recent work on Hybrid, with various specification logics (SLs), including substructural logics, formalized in Isabelle/HOL and used in turn to encode judgments of the object language. We also compare these with a variant that does not use an intermediate SL layer. In the course of the case study, we explore and develop new proof techniques, particularly in connection with context invariants and induction on SL statements.
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Ceragioli, Leonardo. "Pluralism in Proof-Theoretic Semantics." Doctoral thesis, 2020. http://hdl.handle.net/2158/1196477.

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Proof-theoretic semantics is a well-established inferentialist theory of meaning that develops ideas proposed by Prawitz and Dummett. The main aim of this theory is to find a foundation of logic based on some aspects of the linguistic use of the logical terms, as opposed to the regular foundation offered by a model-theoretic approach à la Tarski, in which the denotation of non-linguistic entities is central. Traditionally, intuitionistic logic is considered justified in proof-theoretic semantics (although some doubts are sometimes raised regarding ex falso quodlibet). Even though this approach to semantics has greatly progressed in the last decades, it remains nonetheless controversial the existence of a justification of classical logic that suits its restraints. In this thesis I examine various proposals that try to give such a justification and propose a new one greatly inspired by one of Peter Milne’s papers. The conclusion is, to some extent, open since a reformulation of some notions of proof-theoretic semantics is needed in order to justify classical logic. I conclude the thesis with a general defence of logical pluralism and a description of the kind of pluralism that can be applied to our reformulation of proof-theoretic semantics.
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PICCOLOMINI, d' ARAGONA ANTONIO. "Dag Prawitz's theory of grounds." Doctoral thesis, 2019. http://hdl.handle.net/11573/1359602.

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The dissertation concerns Prawitz's theory of grounds, a constructive, proof-theoretic semantics the aim of which is that of explaining why and how deductively valid inferences are compelling. It is divided into three parts. In the first, we outline Prawitz's previous semantic approach in terms of valid arguments and/or proofs, and show the problems it suffers from when trying to account for the epistemic power of valid inferences. In the second, we illustrate Prawitz's own proposal, and evaluate the advantages it allows for with respect to its basic tasks. Finally, in the third part, we propose a formal development of the theory, in terms of (hierarchies of) languages of grounding, of (hierarchies of) systems of grounds, and with respect to correctness/completeness and decidability issues.
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Books on the topic "Proof-theoretic semantics"

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Piecha, Thomas, and Peter Schroeder-Heister, eds. Advances in Proof-Theoretic Semantics. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22686-6.

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Schroeder-Heister, Peter, and Thomas Piecha. Advances in Proof-Theoretic Semantics. Springer, 2016.

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What Logics Mean: From Proof Theory to Model-Theoretic Semantics. University of Cambridge ESOL Examinations, 2013.

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Tennant, Neil. Core Logic and the Paradoxes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.003.0011.

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The Law of Excluded Middle is not to be blamed for any of the logico-semantic paradoxes. We explain and defend our proof-theoretic criterion of paradoxicality, according to which the ‘proofs’ of inconsistency associated with the paradoxes are in principle distinct from those that establish genuine inconsistencies, in that they cannot be brought into normal form. Instead, the reduction sequences initiated by paradox-posing proofs ‘of ⊥’ do not terminate. This criterion is defended against some recent would-be counterexamples by stressing the need to use Core Logic’s parallelized forms of the elimination rules. We show how Russell’s famous paradox in set theory is not a genuine paradox; for it can be construed as a disproof, in the free logic of sets, of the assumption that the set of all non-self-membered sets exists. The Liar (by contrast) is still paradoxical, according to the proof-theoretic criterion of paradoxicality.
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Tennant, Neil. Core Logic. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.001.0001.

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Core Logic has unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. It is an elegant kernel lying deep within Classical Logic, a canon for constructive and relevant deduction furnishing faithful formalizations of informal constructive mathematical proofs. Its classicized extension provides likewise for non-constructive mathematical reasoning. Confining one’s search to core proofs affords automated reasoners great gains in efficiency. All logico-semantical paradoxes involve only core reasoning. Core proofs are in normal form, and relevant in a highly exigent ‘vocabulary-sharing’ sense never attained before. Essential advances on the traditional Gentzenian treatment are that core natural deductions are isomorphic to their corresponding sequent proofs, and make do without the structural rules of Cut and Thinning. This ensures relevance of premises to conclusions of proofs, without loss of logical completeness. Every core proof converts any verifications of its premises into a verification of its conclusion. Core Logic makes one reassess the dogma of ‘unrestricted’ transitivity of deduction, because any core ‘restriction’ of transitivity ensures a more than compensatory payoff of epistemic gain: A core proof of A from X and one of B from {A}∪Y effectively determine a proof of B or of absurdity from some subset of X∪Y. The primitive introduction and elimination rules governing the logical operators in Core Logic are subtly different from Gentzen’s. They are obtained by smoothly extrapolating protean rules for determining truth values of sentences under interpretations. Core rules are inviolable: One needs all of them in order to revise beliefs rationally in light of new evidence.
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Shapiro, Stewart. Logical Consequence, Proof Theory, and Model Theory. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0021.

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This article's main concern is the notion of model-theoretic consequence. What does it have to do with correct reasoning? The article takes on deductive consequence only by way of contrast. Do these two notions answer to different intuitive notions of consequence? Is one of them primary, and the other secondary? Or perhaps they are autonomous and independent. Maybe there are two distinct notions of correct reasoning, valid thought, and/or inference. For what it is worth, treatments of mathematical logic usually presuppose that the model-theoretic notion is the primary one. For example, one says that a deductive system is sound or complete (or not) for the semantics—not the other way around. If a deductive system is not sound for a given semantics, then that alone disqualifies the deductive system. It is because the deductive system allows us to deduce a falsehood from truths in some interpretation of the language.
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Book chapters on the topic "Proof-theoretic semantics"

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Piecha, Thomas. "Completeness in Proof-Theoretic Semantics." In Advances in Proof-Theoretic Semantics, 231–51. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_15.

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Fichot, Jean. "Proof-Theoretic Semantics and Feasibility." In Logic, Epistemology, and the Unity of Science, 135–57. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-9217-2_5.

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Piecha, Thomas, and Peter Schroeder-Heister. "Advances in Proof-Theoretic Semantics: Introduction." In Advances in Proof-Theoretic Semantics, 1–4. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_1.

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Hallnäs, Lars. "On the Proof-Theoretic Foundations of Set Theory." In Advances in Proof-Theoretic Semantics, 161–71. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_10.

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Hodges, Wilfrid. "A Strongly Differing Opinion on Proof-Theoretic Semantics?" In Advances in Proof-Theoretic Semantics, 173–88. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_11.

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Došen, Kosta. "Comments on an Opinion." In Advances in Proof-Theoretic Semantics, 189–93. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_12.

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Goldfarb, Warren. "On Dummett’s “Proof-Theoretic Justifications of Logical Laws”." In Advances in Proof-Theoretic Semantics, 195–210. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_13.

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Ekman, Jan. "Self-contradictory Reasoning." In Advances in Proof-Theoretic Semantics, 211–29. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_14.

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Schroeder-Heister, Peter. "Open Problems in Proof-Theoretic Semantics." In Advances in Proof-Theoretic Semantics, 253–83. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_16.

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Prawitz, Dag. "On the Relation Between Heyting’s and Gentzen’s Approaches to Meaning." In Advances in Proof-Theoretic Semantics, 5–25. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22686-6_2.

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Conference papers on the topic "Proof-theoretic semantics"

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Francez, Nissim. "A Proof-Theoretic Semantics for Transitive Verbs with an Implicit Object." In Proceedings of the 15th Meeting on the Mathematics of Language. Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/w17-3406.

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Liu, Fangfang, and Jia-Huai You. "Three-Valued Semantics for Hybrid MKNF Knowledge Bases Revisited (Extended Abstract)." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/798.

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Knorr et al. (2011) formulated a three-valued formalism for the logic of Minimal Knowledge and Negation as Failure (MKNF) and proposed a well-founded semantics for hybrid MKNF knowledge bases (KBs). The main results state that if a hybrid MKNF KB has a three-valued MKNF model, its well-founded MKNF model exists, which is unique and can be computed by an alternating fixpoint construction. In this paper, we show that these claims are erroneous. We propose a classification of hybrid MKNF KBs into a hierarchy and show that its innermost subclass is what works for the well-founded semantics of Knorr et al. Furthermore, we provide a uniform characterization of well-founded, two-valued, and all three-valued MKNF models, in terms of stable partitions and the alternating fixpoint construction, which leads to updated complexity results as well as proof-theoretic tools for reasoning under these semantics.
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