20 results for “Formal logic, proof theory, arithmetic, computer science, mathematics”
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The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…
The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…
This paper proves several properties about Extended Frege proof systems and circuit equivalence.
This paper introduces reflective grounded arithmetic (RGA), a paracomplete arithmetic system that permits unconstrained recursive definitions, proves the totality of addition and multiplication, repre…
This paper develops distributive laws for parallel composition in a rely/guarantee style theory for reasoning about concurrent programs.
This paper proves that the satisfiability problem of existential Presburger arithmetic extended with divisibility predicates (EPAD) is PP-hard.
The paper develops a novel, sound, and complete deductive proof system for proving contract satisfaction, which is crucial for verifying CPU security against side-channel attacks.
This paper introduces the concept of 'large' zeros in linear recurrence sequences and establishes that they either do not exist or are very sparse, which could lead to decidability of the Skolem Probl…
This paper introduces dynamic epistemic paraconsistent logics AMLFI1, PALFI1, and UMLFI1, extending the epistemic paraconsistent logics KLFI1, KB4LFI1, and S5LFI1. It proves soundness and completeness…
This paper introduces the because-calculus, a calculus that structurally separates registration and attestation using dual effect rows and level-indexed typing, and proves the Conflation Theorem.
Harrison Grodin, Ethan Chu, Runming Li, Jan Hoffmann +1 more
This paper presents Calf, a dependent type theory for cost verification, which synthesizes the physicist's and banker's views on amortized analysis using potential functions and credit annotations.
This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…
The paper provides a unified algebraic framework to determine the formal language expressivity of recurrent neural language models, resolving conflicts in existing literature by linking expressivity t…