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A logic of interactive proofs [PDF]
Journal of Logic and Computation, 2021 Abstract We introduce the probabilistic two-agent justification logic $\textsf {IPJ}$, a logic in which we can reason about agents that perform interactive proofs. In order to study the growth rate of the probabilities in $\textsf {IPJ}$, we present a new method of parametrizing $\textsf {IPJ}$ over certain negligible functions. Further,
David Lehnherr +2 more
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Logica Universalis, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo Bonelli
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Logic of proofs and provability
Annals of Pure and Applied Logic, 2001 Artemov's logic LP of proofs is extended by adjoining the GL modality so as to incorporate both the modality for provability and the operator representing the proof predicate ``is a proof of''. To formalize the joint logic, two new operations on proof terms are required for the language in addition to the ``application'', ``proof checker'', and ...
exaly +2 more sources
Theoretical Computer Science, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly +4 more sources
Intuitionistic Hypothetical Logic of Proofs
Electronic Notes in Theoretical Computer Science, 2014 AbstractWe study a term assignment for an intuitonistic fragment of the Logic of Proofs (LP). LP is a refinement of modal logic S4 in which the assertion □A is replaced by 〚s〛A whose intended reading is “s is a proof of A”. We first introduce a natural deduction presentation based on hypothetical judgements and then its term assignment, which yields a ...
Eduardo Bonelli
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A full formal representation of Arrow's impossibility theorem. [PDF]
PLoS ONERevised proofs of Kenneth Arrow's impossibility theorem, one of the most influential theorems in economics, political science, and philosophy, have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters.
Kazuya Yamamoto
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ReLoC Reloaded: A Mechanized Relational Logic for Fine-Grained Concurrency and Logical Atomicity [PDF]
Logical Methods in Computer Science, 2021 We present a new version of ReLoC: a relational separation logic for proving refinements of programs with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is its refinement judgment $e \precsim e' : \tau$,
Dan Frumin +2 more
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Multiplicative-Additive Proof Equivalence is Logspace-complete, via Binary Decision Trees [PDF]
Logical Methods in Computer Science, 2017 Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible with its cut ...
Marc Bagnol
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ProoFVer: Natural Logic Theorem Proving for Fact Verification
Transactions of the Association for Computational Linguistics, 2022 Fact verification systems typically rely on neural network classifiers for veracity prediction, which lack explainability. This paper proposes ProoFVer, which uses a seq2seq model to generate natural logic-based inferences as proofs. These proofs consist
Amrith Krishna +2 more
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Towards Coinductive Theory Exploration in Horn Clause Logic: Position Paper [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data.
Ekaterina Komendantskaya Dr, Yue Li
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