Results 1 to 10 of about 167 (167)
Herbrand Proofs and Expansion Proofs as Decomposed Proofs [PDF]
Journal of Logic and Computation, 2020 Abstract The reduction of undecidable first-order logic to decidable propositional logic via Herbrand’s theorem has long been of interest to theoretical computer science, with the notion of a Herbrand proof motivating the definition of expansion proofs.
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Proofs of Proof-of-Stake with Sublinear Complexity
CoRR, 2022 Popular Ethereum wallets (like MetaMask) entrust centralized infrastructure providers (e.g., Infura) to run the consensus client logic on their behalf. As a result, these wallets are light-weight and high-performant, but come with security risks. A malicious provider can mislead the wallet by faking payments and balances, or censoring transactions.
Agrawal, Shresth +3 more
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The Review of Symbolic Logic, 2020 Abstract This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to.
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Different Proofs are Good Proofs
EPiC Series in Computing, 2018 In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine differences between the proofs. This paper discounts the approach of ranking measurements of proof artifacts, and takes the position that different proofs are good proofs.
Geoff Sutcliffe +4 more
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Proofs, Proofs, Proofs, and Proofs [PDF]
, 2010 In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence. Sociologically, however, it is more difficult to say what should constitute a proof and what not.
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Journal of Computer and System Sciences, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander A. Razborov, Steven Rudich
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INFORMAL PROOF, FORMAL PROOF, FORMALISM [PDF]
The Review of Symbolic Logic, 2015 AbstractIncreases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur.
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, 2012 TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual exclusion algorithm as a simple example to describe the features of TLAPS and show how it and the Toolbox (an IDE ...
Cousineau, Denis +5 more
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Gut microbiome and aging—A dynamic interplay of microbes, metabolites, and the immune system
FEBS Letters, EarlyView.Age‐dependent shifts in microbial communities engender shifts in microbial metabolite profiles. These in turn drive shifts in barrier surface permeability of the gut and brain and induce immune activation. When paired with preexisting age‐related chronic inflammation this increases the risk of neuroinflammation and neurodegenerative diseases.
Aaron Mehl, Eran Blacher
wiley +1 more source
When Is a Proof a Proof? [PDF]
, 2020 AbstractIn his famous talk at ICME 2 (Exeter 1972) the French mathematician R. Thom pointed out that any conception of mathematics teaching necessarily rests on a certain view of mathematics (Thom 1973, 204). As a consequence mathematics education cannot develop without close links to mathematics.
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